If climate is viewed as a chaotic dynamical system, its trajectories yielding on an object called attractor. Being perturbed by an external forcing, this attractor could be modified. With Wasserstein distance, we estimate on a derived Lorenz model the impact of a forcing similar to climate change. Our approach appears to work with small data sizes. We have obtained a methodology quantifying the deformation of well known attractors, coherent with the size of data available.