<p>Daily meteorological data such as temperature or precipitation from climate models is needed for many climate impact studies, e.g. in hydrology or agriculture but direct model output can contain large systematic errors. Thus, statistical bias adjustment is applied to correct climate model outputs. Here we review existing statistical bias adjustment methods and their shortcomings, and present a method which we call EQA (Empirical Quantile Adjustment), a development of the methods EDCDFm and PresRAT. We then test it in comparison to two existing methods using real and artificially created daily temperature and precipitation data for Austria. We compare the performance of the three methods in terms of the following demands: (1): The model data should match the climatological means of the observational data in the historical period. (2): The long-term climatological trends of means (climate change signal), either defined as difference or as ratio, should not be altered during bias adjustment, and (3): Even models with too few wet days (precipitation above 0.1 mm) should be corrected accurately, so that the wet day frequency is conserved. EQA fulfills (1) almost exactly and (2) at least for temperature. For precipitation, an additional correction included in EQA assures that the climate change signal is conserved, and for (3), we apply another additional algorithm to add precipitation days.</p>