A Potential Problem with the Application of Moist Static Energy in Tropical Cyclone Studies

The moist static energy (MSE) is derived from the first law of thermodynamics and has been widely used in tropical cyclone (TC) studies because of its energetic and conventionally recognized conservation properties. This study investigates the validation of the MSE application in TC systems based on cloud-resolving numerical simulations. By examining the approximations made in deriving the MSE, neglecting the horizontal advection of pressure (namely, the generation of kinetic energy) relative to the vertical advection of pressure is found to be in error in the boundary layer of TCs with the horizontal advection of pressure even being several times larger than the vertical advection of pressure near the surface. Such a problematic approximation has broken down the conservation property of MSE in adiabatic conditions. An investigation of the energetic characteristics based on an MSE budget equation demonstrates that the MSE has created significant bias in evaluating the energy transport in the inner region of the TC boundary layer. Neglecting the kinetic energy conversion term in the boundary layer leads to a more strengthened cool-pool feature of MSE relative to the equivalent potential temperature; therefore, the interchangeable relationship between these two terms may also be inaccurate in the boundary layer. It is concluded that, although the MSE is an instrumental term for TC studies, caution should be taken when it is used in the boundary layer of TCs.