  The next era of ground-based Cherenkov telescope development will see a great
increase in both quantity and quality of $\gamma$-ray morphological data. This
initiated the development of a spatio-temporal leptonic transport code to model
pulsar wind nebulae. We present results from this code that predicts the
evolution of the leptonic particle spectrum and radiation at different radii in
a spherically-symmetric source. We simultaneously fit the overall broadband
spectral energy distribution, the surface brightness profile and the X-ray
photon index vs.\ radius for PWN 3C~58, PWN G21.5$-$0.9 and PWN G0.9+0.1. Such
concurrent fitting of disparate data sets is non-trivial and we thus
investigate the utility of different goodness-of-fit statistics, specifically
the traditional $\chi^2$ test statistic and a newly developed
scaled-flux-normalised test statistic to obtain best-fit parameters. We find
reasonable fits to the spatial and spectral data of all three sources, but note
some remaining degeneracies that will have to be broken by future observations.
