  The two charge-density wave (CDW) transitions in NbSe$_3$ %at wave numbers at
$\bm{q_1}$ and $\bm{q_2}$, occurring at the surface were investigated by
scanning tunneling microscopy (STM) on \emph{in situ} cleaved $(\bm{b},\bm{c})$
plane. The temperature dependence of first-order CDW satellite spots, obtained
from the Fourier transform of the STM images, was measured between 5-140 K to
extract the surface critical temperatures (T$_s$). The low T CDW transition
occurs at T$_{2s}$=70-75 K, more than 15 K above the bulk T$_{2b}=59$K while at
exactly the same wave number. %determined by x-ray diffraction experiments.
Plausible mechanism for such an unusually high surface enhancement is a
softening of transverse phonon modes involved in the CDW formation.% The large
interval of the 2D regime allows to speculate on % %the special
Berezinskii-Kosterlitz-Thouless type of the surface transition expected for
this incommensurate CDW. This scenario is checked by extracting the temperature
dependence of the order % %parameter correlation functions. The regime of 2D
fluctuations is analyzed according to a Berezinskii-Kosterlitz-Thouless type of
surface transition, expected for this incommensurate 2D CDW, by extracting the
temperature dependence of the order parameter correlation functions.
