Normal Mode Initialization in a Tropical Cyclone Model

Abstract

The effect of nonlinear normal mode initialization (NMI) on tropical cyclone simulations is investigated using a three-layer axisymmetric model. It is shown that the balance condition proposed by Machenhauer, which neglects the time tendencies of the gravity-mode amplitudes, is valid in a tropical cyclone simulation. The boundary layer friction, adiabatic nonlinear and diabatic heating terms are important in the balance. A highly truncated version of the model with linearized physical parameterizations is used to analyze the convergence properties of several iterative schemes developed to solve the initialization equations. When diabatic heating is neglected, the schemes will always converge if the linear friction coefficient α is smaller than the Coriolis parameter f. For small horizontal-scale modes, the iterative schemes will also converge for values of α much larger than f. When diabatic beating is included, the rate of convergence of the small horizontal-scale modes becomes extremely slow. The schemes are also tested in the nonlinear version of the model by first running a 7-day tropical cyclone simulation. The initialization schemes are applied at day 5 after the model has produced an intense tropical cyclone. Results show that the tropical cyclone rapidly weakens relative to the uninitialized run during the 6–12 h after the NMI is applied. This weakening occurs because the small horizontal-scale modes do not converge, making the secondary radial circulation much too weak. A scheme is proposed where the NMI is followed by a short integration with the geostrophic modes held fixed. This procedure compensates for the lack of convergence of the small horizontal-scale gravity modes.