  The model of landscape erosion, introduced in [{\it Phys. Rev. Lett.} {\bf
80}: 4349 (1998); {\it J. Stat. Phys.} {\bf 93}: 477 (1998)] and modified in
[{\it Theor. Math. Phys.} - in press; arXiv:1602.00432], is advected by
anisotropic velocity field. The field is Gaussian with vanishing correlation
time and the pair correlation function of the form $\propto \delta(t-t') /
k_{\bot}^{d-1+\xi}$, where $k_{\bot}=|{\bf k}_{\bot}|$ and ${\bf k}_{\bot}$ is
the component of the wave vector, perpendicular to a certain preferred
direction -- the $d$-dimensional generalization of the ensemble introduced by
Avellaneda and Majda [{\it Commun. Math. Phys.} {\bf 131}: 381 (1990)].
Analogous to the case without advection, the model is multiplicatively
renormalizable and has infinitely many coupling constants. The one-loop
counterterm is derived in a closed form in terms of the certain function
$V(h)$, entering the original stochastic equation, and its derivatives with
respect to the height field $h(t,{\bf x})$. The full infinite set of the
one-loop renormalization constants, $\beta$-functions and anomalous dimensions
is obtained from the Taylor expansion of the counter-term. Instead of a
two-dimensional surface of fixed points there is two such surfaces; they are
likely to contain infrared attractive region(s). If that is the case, the model
exhibits scaling behaviour in the infrared range. The corresponding critical
exponents are nonuniversal because they depend on the coordinates of the fixed
points on the surface; they also satisfy certain universal exact relation.
