This research addresses the current lack of comprehensive, quantitative methods for comparing hydrological spatial fields. Comparison of spatial fields is needed for assessing hydrological models and for data assimilation. The methods that are currently used for quantitative comparison generally fail to consider the spatial arrangement of element values within spatial fields. Instead, there is a dependence on qualitative methods (e.g. visual comparison) to undertake comparison of many aspects (e.g. intermediate scale features), but such methods are non-repeatable, often biased and difficult to report on. At present, the hydrological community continues to develop its ability to observe and model spatial fields, but comprehensive model assessment is still in its infancy. The methods developed in this research provide a new suite of tools to the modeller and, if adopted, can significantly advance the art and science of spatial hydrological modelling.