The advantages of the new generation of radar systems with high resolution image, short revisit time provide the possibility of characterization and monitoring the evolution of the cryoshpere. In this paper, we propose an adaptation of the multilayer snow backscattering model based on radiative transfer theory in order to estimate the total backscattering coefficient of high frequency (X-band) electromagnetic wave on snowcover area. Next, from the physical model, we develop the adjoint operator and implement a variational assimilation scheme in order to constrain the snow stratigraphy profiles calculated by CROCUS, a snow metamorphism model used by MeteoFrance. Some tests are carried out with TerraSAR-X image data. The results show that the snow stratigraphy profiles obtained after the data assimilation process have good agreement with the measured profiles, and therefore show the high potential of this method in constraining the snowpack profiles of CROCUS.