A major challenge in assessing the impacts of climate change on hydrological processes lies in dealing with large degrees of uncertainty in the future climate projections. Part of the uncertainty is owed to the intrinsic randomness of climate phenomena, which is considered irreducible. Additionally, modelling the response of hydrological processes to the changing climate requires the use of a chain of numerical models, each of which contributes some degree of uncertainty to the final outputs. As a result, hydrological projections, despite the progressive increase in the accuracy of the models along the chain, still display high levels of uncertainty, especially at small temporal and spatial scales. In this work, we present a framework to quantify and partition the uncertainty of hydrological processes emerging from climate models and internal variability, across a broad range of scales. Using the example of two mountainous catchments in Switzerland, we produced high-resolution ensembles of climate and hydrological data using a two-dimensional weather generator (AWE-GEN- 2d) and a distributed hydrological model (TOPKAPI-ETH). We quantified the uncertainty in hydrological projections towards the end of the century through the estimation of the values of signal-to-noise ratios (STNR). We found small STNR absolute values (<1) in the projection of annual streamflow for most sub-catchments in both study sites that are dominated by the large natural variability of precipitation (explains ~70% of total uncertainty). Furthermore, we investigated in detail specific hydrological components that are critical in the model chain. For example, snowmelt and liquid precipitation exhibit robust change signals, which translates into high STNR values for streamflow during warm seasons and at higher elevations, together with a larger contribution of climate model uncertainty. In contrast, projections of extreme high flows show low STNR values due to large internal climate variability across all elevations, which limits the potential for narrowing their estimation uncertainty.