  A new ''static'' renormalization group approach to stochastic models of
fluctuating surfaces with spatially quenched noise is proposed in which only
time-independent quantities are involved. As examples, quenched versions of the
Kardar-Parisi-Zhang model and its Pavlik's modification, the Hwa-Kardar model
of self-organized criticality, and Pastor-Satorras-Rothman model of landscape
erosion are studied. It is shown that the upper critical dimension in the
quenched models is shifted by two units upwards in comparison to their
counterparts with white in-time noise. Possible scaling regimes associated with
fixed points of the renormalization group equations are found and the critical
exponents are derived to the leading order of the corresponding
epsilon-expansions. Some exact values and relations for these exponents are
obtained.
