Climatic extremes are changing and decision-makers express a strong need for reliable information on future changes over the coming decades as a basis for adaption strategies. In the hydrological-hydraulic context, to estimate changes on floods, a modeling chain composed by general circulation models (GCMs), bias correction (BC) methods, and hydrological modeling is generally applied. It is well-known that each step of the modeling chain introduces uncertainties, resulting in a reduction of the reliability of future climate projections. The main goal of this study is the assessment of the accuracy and variability (i.e., model accuracy, climate intermodel variability, and natural variability) on climate projections related to the present period. By using six different GCMs and two BC methods, the "climate intermodel variability" is evaluated. "Natural variability" is estimated through random realizations of stochastic weather generators. By comparing observed and simulated extreme discharge values, obtained through a continuous rainfall-runoff model, "model accuracy" is computed. The Tiber River basin in central Italy is used as a case study. Results show that in climate projections, model accuracy and climate intermodel variability components have to be clearly distinguished. For accuracy, the hydrological model is found to be the largest source of error; for variability, natural variability contributes for more than 75% to the total variability while GCM and BC have a much lower influence. Moreover, accuracy and variability components vary significantly, and not consistently, between catchments with different permeability characteristics.