Sensitivity of Simulated Axisymmetric Tropical Cyclones to Numerical Implicit Diffusion

The intensity of simulated tropical cyclones (TCs) has been shown to be very sensitive to a number of model parameters like the surface enthalpy and momentum exchange coefficients. Additionally, simulated axisymmetric TCs are very sensitive to parameterized mixing, which acts to weaken the eyewall gradients of entropy and momentum. TC potential intensity (PI) theories like those of Emanuel (1986) or Bryan and Rotunno (2009) assume axisymmetric and inviscid flow, and verification of such theories requires the use of axisymmetric models with low parameterized mixing, to simplify the comparison. However, TCs are frontogenetic systems, and in finite volume or finite difference models, either parameterized or numerical implicit diffusion must act to prevent collapse of the eyewall front to the grid scale. It may be tempting to consider simulations with low parameterized mixing as nearly inviscid, but simulations using the model CM1 in axisymmetric configuration show that, as parameterized mixing becomes small, implicit diffusion becomes dominant, stopping the collapse of the front. Analysis using budget equations for momentum, integrated along streamlines, show that at low parameterized mixing, implicit diffusion is responsible for variations of up to 15% of the angular momentum of a parcel, as it ascends through the eyewall. This increased importance of numerical implicit diffusion suggests an increased sensitivity of TC intensity to numerical parameters such as the order of the advection scheme. These results may explain why different numerical models produce different maximum TC intensity, since models use various numerical techniques that likely have different levels of implicit diffusion.