Inconsistencies Exhibited by Simulated Parcel Trajectories below the Lowest Scalar Model Level

Analysis of modeled parcel trajectories has become commonplace in the study of convective dynamics. While advances in computing has precipitated the development of cloud models capable of realistically simulating convection at high spatial and temporal resolution—and are thus capable of simulating parcel trajectories with a high degree of realism—the treatment of parcels beneath the lowest model level in vertically staggered model grids continues to be an unsolved problem for a number of reasons. First, the horizontal wind profile beneath the lowest model level cannot be determined by the prognostic equations of the model, and therefore must be parameterized analytically. Second, the profile of non-velocity scalar quantities (e.g. potential temperature, mixing ratio, etc.) are similarly unknown beneath the lowest model level such that a convention to assign non-velocity scalar values along parcel trajectories that descend below the lowest scalar model level must be specified.

In the zero-gradient free-slip boundary condition, there are an infinite number of possible profiles of the horizontal wind and scalar profiles beneath the lowest scalar model level. Because of this, without observational guidance, it is difficult to determine if one treatment of parcels that are beneath the lowest scalar model level is better than another, and nearly impossible to know if that treatment produces a physically correct solution. Furthermore, it is shown that model variables must be extrapolated from the model grid to parcels below the lowest scalar model level—as opposed to interpolated from the model grid if the parcel is located above the lowest scalar model level. Because of this, the portion of a trajectory that is below the lowest scalar model level is inconsistent with the portion of the trajectory that is above the lowest scalar model level. Such an inconsistency can result in the unphysical evolution of the model variables and location while a parcel is below the lowest scalar model level.

Without observational data to guide the estimation of the vertical profile of model variables below the lowest scalar model level, such inconsistencies along parcel trajectories below the lowest scalar model level are unavoidable. In order to reduce the possibility of contaminating any parcel trajectory interpretation, great care must be taken when analyzing any parcels which spend time below the lowest scalar model level along their trajectories.