The Mesoscale and Microscale Structure and Organization of Clouds and Precipitation in Midlatitude Cyclones. Part XV: A Numerical Modeling Study of Frontogenesis and Cold-Frontal Rainbands

A two-dimensional, hydrostatic, primitive-equation model is used to investigate the dynamics of frontogenesis in a moist atmosphere. The development of a cold front is simulated through shear-deformation associated with the non-linear evolution of an Eady wave. Simulations are performed with 5, 10, 40 and 80 km horizontal resolutions and 14 levels in the vertical (four in the boundary layer). Compared to the dry case, the inclusion of moisture in the model produces a stronger low-level jet ahead of the front and a stronger upper-level jet. Moisture also produces a stronger ageostrophic circulation across the front and a more concentrated updraft just ahead of the surface front. The updraft develops a banded structure above and behind the surface front, with a wavelength of about 70 km. Bands form near the back edge of the cloud shield and move toward the surface front with a relative velocity of ∼1 m s−1. These characteristics agree with observations of wide cold-frontal rainbands. The banded structures form in a convectively stable region. The first band that appears in the numerical simulation forms and intensifies in a region of negative equivalent potential vorticity. Subsequent bands form behind the first and intensify as they move into the region of negative equivalent potential vorticity, indicating that conditional symmetric instability (CSI) may play an important role in their formation and intensification. Many of the characteristics of the bands agree with the theory of CSI. The bands disappear when equivalent potential vorticity is everywhere positive. The bands are poorly resolved when the horizontal resolution (Δx) of the model is 40 km, and they are absent with Δx = 80 km. However, the strength and horizontal scale of the bands is about the same with Δx = 5 km and Δx = 10 km. This indicates that the banded structure is not an artifact of the model. Frictional convergence in the boundary layer forces a narrow cold-frontal rainband (NCFR) just above the surface front. The horizontal dimension of this band is greater than that for observed NCFR, presumably because of limited resolution in the model.