One of the questions that climate modellers should address is whether their models have sufficient spatial resolution to resolve the physical processes affecting climate. This paper addresses this question using the Hadley Centre climate model, HadAM3 (the climate version of the Met Office's Unified Model). The model is run in AMIP II mode at 4 resolutions ranging from N48 (2.5 x 3.75 deg) to N144 (0.833 x 1.25 deg). An inherent assumption in this approach, and in numerical modelling of the atmosphere generally, is that models will converge towards an ideal solution as resolution is increased - provided we stay within the range for which the parametrizations are valid. We will show that this assumption is not always justified. In principle, undesirable resolution dependencies in physical parametrizations can be removed. However, many processes, such as convection, are inherently non-linear making resolution dependency inevitable. We will show that even in a dynamical core of our model, non-linear and non-local dynamics mean that certain aspects of the results do not converge when resolution is increased.