Horizontal advection discretization: advective form

When using the non-hydrostatic option, the horizontal advection of $\varphi$ is required, and it is in advective form. The fourth order advection of a variable $\varphi$ in advective form can be written as

$$\left({U \frac{\partial\varphi}{\partial x}}\right)_i = \frac{1}{... ...} \left(-\varphi_{i+1}+9\varphi_{i}-9\varphi_{i-1}+\varphi_{i-2}\right) \right]$$ (152)