MM5 is based on primitive physical equations of momentum, thermodynamics, and conservation. The state variables are temperature, specific humidity, grid-relative wind components, and pressure. In the prognostic equations, the state variables are mass-weighted with a modified surface pressure. MM5 can be run as either a hydrostatic or non-hydrostatic model. In the hydrostatic model, the state variables are explicitly forecast. In the non-hydrostatic model [Dudhia, 1993], pressure, temperature, and density are defined in terms of a reference state and perturbations from the reference state. The vertical (sigma) coordinate is defined as a function of pressure.
The hydrostatic and non-hydrostatic versions of MM5 use different time differencing schemes to filter the fast waves from the prognostic solutions in the model. In the non-hydrostatic model, a semi-implicit scheme based on Klemp and Wilhelmson [1978] is used to filter the acoustic waves from the model solution. In the hydrostatic model, a split-explicit scheme based on Madala [1981] is used to filter gravity waves from the model solution. The time differencing in MM5 is extensively discussed in Grell et al. [1995.
There are five options for lateral boundary conditions in MM5: fixed, relaxation, time dependent, time dependent and inflow/outflow dependent, and sponge. The lateral boundaries in MM5 consist of the outer five grid points on the horizontal perimeter of the simulation domain. (The outer four grid points are used for boundary conditions for “cross” point variables.) The lateral boundary conditions for the coarse domain are derived from the meteorological background fields processed in REGRID and INTERP. For the nests (when the one-way nest option is selected), the lateral boundary conditions are interpolated from the simulation on the parent domain.