Fig. 1.

(Slope, wavenumber)-Busse balloon slices for the extended-Klausmeier model for two different values of the rainfall parameter $a$. A banded pattern solution to the extended-Klausmeier model with slope $v$ and wavenumber $k$ is stable if the $\left(v,k\right)$ combination lies inside the Busse balloon. This indicates that a wide spread of $\left(v,k\right)$ combinations yields stable banded patterns. The latter are therefore expected for a broad range of wavenumbers—and not for specific $\left(v,k\right)$ choices only. The shape of a Busse balloon can change between models and between parameter values. This is illustrated in A and B, which were computed for different $a$ values. Model parameters used are $e=500,m=0.45,$ and $a=3.0\left(A\right)$ or $a=2.5\left(B\right)$.