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.
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