On the use of reduced grids in conjunction with the Equator-Pole grid system

Reduced lat-lon grids with n = 360 and K segments on a hemisphere, using method I. Let N_K be the total number of discretisation points for given K, p_K is the decrease in per cent of N₁, that is $N_K=(1-p_K/100)N_1,$ and the quantity s_i is the number of parallels in the segment $S_i^d.$ The area of the polar regions as per cent of the total area of the sphere is given by $q_K=100(1-\hspace{0.17em}\text{sin}\hspace{0.17em}{\theta }_K).$

Let N be the total number of discretisation points and s_i the number of parallels in the segment $S_i^d.$ The areas of the polar regions as per cent of the total area of the sphere is given by $q_{10}=100(1-\hspace{0.17em}\text{sin}\hspace{0.17em}{\theta }_{10}).$

Normalised errors for solid rotation of the Cosine bell, n = 360, $\Delta t=600$ s, T = 12 days, $\alpha =\pi /3,$ and minimisation over c.

Normalised errors for time dependent flow(Läuter), ${\overline{\mathcal{\ell }}}_2({\Psi }^{*},15)$ minimised over c, n = 360, T = 15 days, $\alpha =\pi /4.$

Normalised errors for time dependent flow(Läuter), ${\overline{r}}_e(15)$ minimised over c, n = 360, $2p=6,\Delta t=300$ s, T = 15 days, $\alpha =\pi /4.$

Zonal flow over an isolated mountain, ${\theta }_c={30}^o,$ n = 360, K = 3, $\Delta t=300,$ T = 15 days, 6 or 4 before ${\overline{r}}_m(15)$ or ${\overline{r}}_e(15)$ denotes the approximation order.

The mountain problem, ${\theta }_c={30}^o,$ n = 360, K = 3, $\Delta t=300,$ T = 5 years.