All Earth System Models (ESMs) have climatological biases relative to the observed historical climate. The quality of a model and, more importantly, the accuracy of its predictions are often associated with the magnitude and properties of its biases. For more than a decade, new strategies have been developed to empirically reduce such biases in the model components of ESMs during their execution. The present study considers a cyclostationary class of empirical runtime bias corrections to a climate model, referred to here as ERBCs. Such ERBCs are state independent and designed to reduce biases in the climatological annual cycle of the model. We present a new procedure for deriving such ERBCs called Climatological Adaptive Bias Correction (CABCOR). CABCOR is argued to be superior to the standard relaxation approach to defining ERBCs because it requires only a climatological, rather than a multi-year time evolving, observational reference dataset. Additionally, it is demonstrated that the CABCOR approach can produce bias-corrected models with smaller climatological biases than the relaxation approach. This is determined by performing a systematic analysis of the biases produced by ERBCs derived with each approach.