To isolate the dynamical and thermodynamic effects of the boundary layer dynamics, three different models with different complexities are used to conduct a series of sensitivity experiments with varying drag coefficient. In this part I, results from a simplified framework, which is a height-resolving boundary layer model coupled with a one layer shallow water equation model above, are discussed in details. In this coupled interactive system, mass sink is parameterized by mass flux at the top of the boundary layer to mimic the eyewall heating and thus to allow intensification of the TC vortex and changes in the radial distribution of gradient wind. Our results demonstrate that the storm with larger drag coefficient, less strength, and higher intensity displays faster eyewall contraction and more rapid intensification of the TC. The relative importance of the dynamical and thermodynamic effects evaluated in a full-physics model will be presented in a companion presentation (part II).