Quasi-Compressible Approximation

Start with Equation of State:

Substitute into Definition of Exner Function

to get Exner Function Equation of State:

Log Differentiate:

With a little manipulation:

Quasi-Compressible Exner Function Equation

Mach Number Check:

Mean Pressure Adjustment

For a limited area model - set mean pressure to constant.
For a 1 way nest within another model or analysis - set mean pressure to mean pressure of outer nest.