Using the non-hydrostatic Penn State/National Center for Atmospheric Research mesoscale model (MM5), a series of experiments was conducted to learn the influence on SJV mixing depths due to several factors: model physics, numerics and data assimilation. All experiments covered the polluted episode from 2 - 6 August 1990 during the SARMAP study and used model domains having 36-km, 12-km and 4-km meshes. For the physics, the non-local Blackadar scheme and a 1.5-order turbulent-kinetic-energy (TKE) predicting boundary layer scheme were used alternatively. For the numerics, experiments were run with and without a 108-km outer mesh, with different sizes of 4-km domain, and with either 32 or 62 vertical layers. For the data-assimilation tests, runs were made with and without careful detailed initialization of the shallow marine boundary layer, and with alternative four-dimensional data assimilation (FDDA) strategies used on the 36-km and 12-km domains (no FDDA was used on the 4-km domain). Comparisons of the 4-km solutions revealed that the choice of the type of boundary-layer scheme and the vertical resolution were the two most important factors needed to correctly simulate the shallow mixing depths in the SJV. The unusually shallow boundary layer of the valley appears to result primarily from subsidence in the return branch of the local mountain-valley circulations of this region. When air-stagnation occurs, subsided air from a prior day may remain over the valley, so that the next day's circulation causes further subsidence heating. Consequently, the afternoon mixing depths were found to decline steadily during the four-day simulation period.