  The characteristic formalism in numerical relativity, which has been
developed to study gravitational waves, and the observer metric approach in
observational cosmology both make use of coordinate systems based on null
cones. In this paper, these coordinate systems are compared and it is then
demonstrated how characteristic numerical relativity can be used to investigate
problems in observational cosmology. In a numerical experiment using the
characteristic formalism, it is shown how the historical evolution of a LTB
universe compares to that of the $\Lambda$CDM model given identical
observational data on a local observer's past null cone. It is demonstrated
that, at an earlier epoch of the LTB model, the observational data would not be
consistent with that of the $\Lambda$CDM model.
