ABSTRACT The next era of ground-based Cherenkov telescope development will see a great increase in both quantity and quality of γ-ray morphological data. This initiated the development of a spatiotemporal 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 broad-band spectral energy distribution, the surface brightness profile, and the X-ray photon index versus 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 χ2 test statistic and a newly developed scaled-flux-normalized test statistic to obtain best-fitting 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.