This paper employs stochastic analysis to investigate the combined effect of temporal and spatial variability on the temporal variance of baseflow in large catchments. The study makes use of the well-known aggregated reservoir model, representing the catchment as a network of parallel linear reservoirs. Each reservoir models a sub-catchment as an independent unit whose discharge temporal variation is characterized by a response time. By treating the rainfall-generated recharge and the sub-catchment response times as random variables, the statistical temporal moments of total baseflow are quantified. Comparisons are made between the temporal variance of baseflow in the aggregated reservoir model and that of a single homogeneous reservoir to define an upscaled response time. The analysis of the statistical moments of the random baseflow reveals that the number of reservoirs N has a weak impact on baseflow variance, with ergodic conditions achieved even with a small number of reservoirs. The study highlights that the ratio between the recharge correlation time and the geometric mean of the sub-catchment response times plays a critical role in baseflow damping and the upscaled response. The results indicate that the dynamics of baseflow generation depend not only on the catchment hydro-geological structure but also on the variability of the input signal. This research underscores the importance of understanding the combined influences of hydro-geological factors and recharge input variability for baseflow prediction under uncertainty. The present study should be regarded as a first step, setting the theoretical framework for future research toward incorporating field data.