AbstractClimate change impact research and risk assessment require accurate estimates of the climate change signal (CCS). Raw climate model data include systematic biases that affect the CCS of high-impact variables such as daily precipitation and wind speed. This paper presents a novel, general, and extensible analytical theory of the effect of these biases on the CCS of the distribution mean and quantiles. The theory reveals that misrepresented model intensities and probability of nonzero (positive) events have the potential to distort raw model CCS estimates. We test the analytical description in a challenging application of bias correction and downscaling to daily precipitation over alpine terrain, where the output of 15 regional climate models (RCMs) is reduced to local weather stations. The theoretically predicted CCS modification well approximates the modification by the bias correction method, even for the station–RCM combinations with the largest absolute modifications. These results demonstrate that the CCS modification by bias correction is a direct consequence of removing model biases. Therefore, provided that application of intensity-dependent bias correction is scientifically appropriate, the CCS modification should be a desirable effect. The analytical theory can be used as a tool to 1) detect model biases with high potential to distort the CCS and 2) efficiently generate novel, improved CCS datasets. The latter are highly relevant for the development of appropriate climate change adaptation, mitigation, and resilience strategies. Future research needs to focus on developing process-based bias corrections that depend on simulated intensities rather than preserving the raw model CCS.