It is well known that climate model output data cannot be used directly as input to impact models, e.g., hydrology models, due to climate model errors. Recently, it has become customary to apply statistical bias correction to achieve better statistical correspondence to observational data. As climate model output should be interpreted as the space-time average over a given model grid box and output time step, the status quo in bias correction is to employ matching gridded observational data to yield optimal results. Here we show that when gridded observational data are not available, statistical bias correction can be carried out using point measurements, e.g., rain gauges. Our nonparametric method, which we call scale-adapted statistical bias correction (SABC), is achieved by data aggregation of either the available modeled or gauge data. SABC is a straightforward application of the well-known Taylor hypothesis of frozen turbulence. Using climate model and rain gauge data, we show that SABC performs significantly better than equal-time period statistical bias correction.