Characterizing the perturbation of scattering coefficients by an additive noise is a key problem to understanding the channel model for a Nonlinear Fourier Transform (NFT) based fibre optical transmission system. In this paper, we show numerically that the perturbation of scattering coefficients is mainly contributed by the noise component (which has significantly lower power than the overall noise) from a dominating noise subspace. An explicit characterization of the subspace is obtained by approximating the derivatives of the scattering coefficients.