Raster spatial datasets are often analyzed at multiple spatial resolutions to understand natural phenomena such as global climate and land cover patterns. Given such datasets, a collection of user defined resolutions and a neighborhood definition, resolution sensitivity analysis (RSA) quantifies the sensitivity of spatial autocorrelation across different resolutions. RSA is important due to applications such as land cover assessment where it may help to identify appropriate aggregations levels to detect patch sizes of different land cover types. However, Quantifying resolution sensitivity of spatial autocorrelation is challenging for two important reasons: (a) absence of a multi-resolution definition for spatial autocorrelation and (b) possible non-monotone sensitivity of spatial autocorrelation across resolutions. Existing work in spatial analysis (e.g. distance based correlograms) focuses on purely graphical methods and analyzes the distance-sensitivity of spatial autocorrelation. In contrast, this paper explores quantitative methods in addition to graphical methods for RSA. Specifically, we formalize the notion of resolution correlograms(RCs) and present new tools for RSA, namely, rapid change resolution (RCR) detection and stable resolution interval (SRI) detection. We propose a new RSA algorithm that computes RCs, discovers interesting RCRs and SRIs. A case study using a vegetation cover dataset from Africa demonstrates the real world applicability of the proposed algorithm.