The model of landscape erosion, introduced in (1998 Phys. Rev. Lett. 80 4349, 1998 J. Stat. Phys. 93 477) and modified in (2016 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 $\propto \delta \left(t-{{t}^{\prime}}\right)/k_{\bot}^{d-1+\xi}$ , where ${{k}_{\bot}}=|{{\mathbf{k}}_{\bot}}|$ and ${{\mathbf{k}}_{\bot}}$ 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 (1990 Commun. Math. Phys. 131 381). 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 $h\left(t,\mathbf{x}\right)$ . The full