The most common use of the method is to utilize gridded longwave radiation estimates produced by an external model, for example, a dynamic atmospheric model. If a gridded longwave radiation estimate is used with a transform method other than ModClark, an area-weighted average of the grid cells in the subbasin is used to compute the longwave radiation time-series for each subbasin.

The atmospheric models used for research, weather, climate and air quality forecasting use integration of the main equations governing atmospheric behavior. These equations include the gas law, the continuity of mass, the first law of thermodynamics (heat), and Navier Stokes equations. All popular atmospheric models solve the Navier-Stokes equation numerically. 

Two prinicipal numerical methods for solving the Navier Stokes equation are the finite-difference method and spectral method. The partial time derivatives and the partial spatial derivatives in the Navier-Stokes equation can be approximated by finite differences. The spectral method uses the Fourier's theorem which states that any periodic signal can be expanded as a Fourier series which is a summation of sine and cosine waves.

An overview of atmospheric models and governing numerical equations can be found here: Atmospheric Model Overview.