Modelling extreme storm severity is critical to design and reliable operation of marine structures. Extreme hindcast storm peak significant wave heights (HS) for 816 locations throughout the North Sea are modelled, using the four parameter Poisson point process model of Wadsworth et al. (2010), incorporating measurement scale variability via a BoxCox transformation. The model allows estimation of the posterior distribution for measurement scale parameter and point process parameters within a Bayesian framework. The effect of measurement scale on return values of significant wave height (HS) is quantified by comparison with a three parameter Poisson point process model ignoring measurement scale uncertainty. It is found that the median value (over all locations) of the median posterior BoxCox parameter (per location) is approximately 0.7, suggesting that the appropriate measurement scale for extreme value analysis is HS0.7. The value of the median BoxCox parameter (per location) varies considerably between locations, with a 90% uncertainty band of approximately (0.2, 2.2) and quartiles of 0.4 and 1.2; the value of BoxCox parameter is also influenced by threshold choice for extreme value analysis in particular. The ratio (over all locations) of the (posterior median) return value from the four parameter model to the return value from the three parameter model (and a return period of 100 times the period of the hindcast) has a median value of 0.92, suggesting that median return values may be reduced for this data set by better modelling of measurement scale effects. The ratio of return values has a 90% uncertainty band of approximately (0.72, 1.37), illustrating the extra variability in return values that incorporation of measurement scale uncertainty introduces. © 2012 Elsevier Ltd. All rights reserved.