### Table 3: Results for the rotating Gaussian hill for the spectral element and spectral element semi-Lagrangian methods for various on a structured grid with the CN scheme.

"... In PAGE 13: ...-type method (i.e., when the polynomial order N is increased rather than the number of elements NE). Table3 shows how the methods are a ected by increasing the Courant number ( ) and hence the time step. The SEM-SLM method performs better at these larger thereby making this method more e cient.... ..."

### Table 2: Results for the rotating Gaussian hill for the spectral element and spectral element semi-Lagrangian methods for =0:5 on a structured grid with the CN scheme.

### Table 4: Results for the Rossby soliton wave problem at t=40 for the spectral element and spectral element semi-Lagrangian methods on a structured grid with t x = 1 15 and the AB

"... In PAGE 17: ...2.2 Structured Grid Table4 shows the results on a structured grid with the AB scheme. These results show that the SEM-SLM works better than the h-type SEM and only slightly better than the p-type SEM.... ..."

### Table 1 Efficiency of the global model on the Earth Simulator

"... In PAGE 1: ... An introduction of the two-time level integration to the semi-Lagrangian scheme increased the efficiency by two times. Table1 shows the efficiency of the present global model on the Earth Simulator. The TL959 version attained 35% of the peak performance of the Earth Simulator.... ..."

### Table 6.2: Errors of semi-Lagrangian method with exact integration of trajectories in solid body rotation test.

in Contents

### Table 6.3: Errors of semi-Lagrangian method with approximate integration of trajectories in solid body rotation test.

in Contents

### Table 7.1: Convergence test for semi-Lagrangian and Lax Wendroff method (one dimensional advection).

in Contents

### Table 9.1: Errors of semi-Lagrangian method with respect to mass conservation in one dimensional test (Courant number a61 a28

in Contents

### Tables 2 and 3 compare the area loss (or gain) of the original high-order accurate particle level set method to the newly proposed semi-Lagrangian based particle level set method on three difierent grids. A CFL number of 4.9 is used on all grids for the semi-Lagrangian calculation, while a CFL number of .5 is used in all HJ-WENO based calculations. The area is calculated using a second order accurate unbiased level set contouring algorithm [3]. In addition, we calculate the accuracy of the interface location using the flrst order accurate error measure introduced in [22],

2005

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