  Standard field theoretic renormalization group is applied to the model of
landscape erosion introduced by R. Pastor-Satorras and D. H. Rothman [Phys.
Rev. Lett. 80: 4349 (1998); J. Stat. Phys. 93: 477 (1998)] yielding unexpected
results: the model is multiplicatively renormalizable only if it involves
infinitely many coupling constants ( i.e., the corresponding renormalization
group equations involve infinitely many beta-functions). Despite this fact, the
one-loop counterterm can be derived albeit 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 $h$. Its Taylor expansion gives
rise to the full infinite set of the one-loop renormalization constants,
beta-functions and anomalous dimensions. Instead of a set of fixed points,
there is a two-dimensional surface of fixed points that is 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 through the dependence on the coordinates of the fixed point on
the surface, but satisfy certain universal exact relations.
