Climate sensitivity is commonly taken to refer to the equilibrium change in the annual mean global surface temperature following a doubling of the atmospheric carbon dioxide concentration. Evaluating this variable remains of significant scientific interest, but its global nature makes it largely irrelevant to many areas of climate science, such as impact assessments, and also to policy in terms of vulnerability assessments and adaptation planning. Here, we focus on local changes and on the way observational data can be analysed to inform us about how local climate has changed since the middle of the nineteenth century. Taking the perspective of climate as a constantly changing distribution, we evaluate the relative changes between different quantiles of such distributions and between different geographical locations for the same quantiles. We show how the observational data can provide guidance on trends in local climate at the specific thresholds relevant to particular impact or policy endeavours. This also quantifies the level of detail needed from climate models if they are to be used as tools to assess climate change impact. The mathematical basis is presented for two methods of extracting these local trends from the data. The two methods are compared first using surrogate data, to clarify the methods and their uncertainties, and then using observational surface temperature time series from four locations across Europe.