  We introduce a self-organized surface growth model in 2+1 dimensions with
anisotropic avalanche process, which is expected to be in the universality
class of the anisotropic quenched Kardar-Parisi-Zhang equation with alternative
signs of the nonlinear KPZ terms. It turns out that the surface height
correlation functions in each direction scales distinctively. The anisotropic
behavior is attributed to the asymmetric behavior of the quenched KPZ equation
in 1+1 dimensions with respect to the sign of the nonlinear KPZ term.
