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Understanding and predicting the evolution of the tropical cyclone (TC) inner-core continues to be a major research focus in tropical meteorology. Eyewall slope and its relationship to intensity and intensity change is one example that has been insufficiently studied. Accordingly, in this study, we use radar reflectivity data to quantify and analyze the azimuthal average and variance of eyewall slopes from 123 flight legs among 15 Atlantic TCs from 2004-2011. The slopes from each flight leg are averaged into 6-h increments around the Best-Track times to allow for a comparison of slope and Best-Track intensity. We find a statistically significant relationship between both the azimuthal mean slope and pressure and between slope and wind. In addition, several individual TCs show higher correlation between slope and intensity. We also find a correlation between slope and radar-based eye size at 2 km, but size shows little correlation with intensity. Large azimuthal variation in eyewall slope is observed in most cases. Some of this variance is apparently due to a tendency for the eyewall to tilt downshear by an average of approximately 10 degrees, and other possible causes for azimuthal variance (such as convective asymmetries) are a subject for future work. In addition, the upper eyewall slopes more sharply than the lower eyewall in about three-fourths of the cases, which is consistent with expected results from thermal wind balance in a warm-core vortex. Analysis of case studies discusses the potential effects on eyewall slope of both inner-core and environmental processes. Hurricane Felix shows a case where the eyewall becomes more upright as the storm strengthens. Hurricane Ivan, on the other hand, shows a case where a secondary eyewall weakens the inner eyewall and causes it to be more tilted, although the intensity does not change immediately. Finally, Hurricane Earl is an example that highlights the systematic tendency for downshear slope. In order to investigate modeled TC structure and compare it with the results from observations, the study also included an analysis of slope in the operational HWRF model. The results of this model analysis illustrate that while HWRF does show a sloping eyewall, it does not seem to capture the observed nature of eyewall slope and structure, at least for the limited sample size of a few cases from the 2012 hurricane season (including a case study of Isaac). The HWRF seems to show eyes that are too large and eyewalls that are too tilted (especially in the upper troposphere). The reasons for this problem are not clear from this study, but possibilities include model physics or even a grid spacing issue due to the finite differencing resolution. The combined results from this study indicate that eyewall slope is an important measure that is intimately related to changes in TC inner-core structure, and may prove useful for future study of the processes that drive such changes in core structure.