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Lack of hydro-bio-chemical data at subcatchment scales necessitates adopting an aggregated system approach for estimating water and solute transport properties, such as residence and travel time distributions, at the catchment scale. In this work, we show that within-catchment spatial heterogeneity, as expressed in spatially variable discharge-storage relationships, can be appropriately encapsulated within a lumped time-varying stochastic Lagrangian formulation of transport. This time (variability) for space (heterogeneity) substitution yields mean travel times (MTTs) that are not significantly biased to the aggregation of spatial heterogeneity. Despite the significant variability of MTT at small spatial scales, there exists a characteristic scale above which the MTT is not impacted by the aggregation of spatial heterogeneity. Extensive simulations of randomly generated river networks reveal that the ratio between the characteristic scale and the mean incremental area is on average independent of river network topology and the spatial arrangement of incremental areas.

Plain Language Summary The absence of rigorous data and theories for extrapolating information from the field to the larger scales necessitates developing reduced-complexity frameworks that are still able to explain the spatial heterogeneity and process complexity in real-world catchments. In this study, we examined the ability of the lumped stochastic Lagrangian formulation for water and solute transport in providing reliable estimates of the mean travel time (MTT) in spatially heterogeneous catchments. Via numerical simulations of heterogeneous catchments, we showed that a time-varying travel time distribution formulation results in MTTs that are not significantly biased to the aggregation of spatial heterogeneity under different age sampling assumptions. This finding reinforces the importance of such a time-variant lumped formalism to appropriately predict the catchment's mean transport time scales without the need to explicitly characterize and embed the small-scale spatial heterogeneity. We also showed that although significant variability of MTT exists at small spatial scales, there exists a characteristic spatial scale above which the MTT converges to a constant value not influenced by the aggregation of spatial heterogeneity. The above findings have practical implications pertaining to data measurements in the field and inferences that can be made on transport time scales and mixing processes across spatial scales.