Climate data plays a crucial role in water resources management, which is becoming an increasingly relevant asset in all types of hydrological analysis not only for climate change studies but for various horizon forecasting. Though the ever-improving accuracy of climate models' spatial and temporal resolution has surged the validity of their outputs, the products of global and regional climate models need to be corrected to be reliably used for local purposes. Here, we propose a comprehensive analysis of statistical univariate and multivariate, as well as machine learning methods for bias correction, which are compared on different temporal scales, ranging from hourly time steps to monthly aggregations, in an environment of complex Alpine orthography, using ERA5-Land reanalysis data. The results reveal different trends in the performance of the bias correction methods for precipitation and temperature across the various time resolutions.