The transport of solutes in stream corridors is an important process for riverine biogeochemistry and ecosystem services. This process is largely controlled by bulk movement in the stream channel and mass exchange with the hyporheic zone. However, modeling solute transport in stream corridors under dynamic hydrological conditions remains a scientific challenge. Here, we extend a steady-state Lagrangian multiscale river-corridor transport model to accommodate unsteady flow. The extended numerical model was evaluated with observations of conservative tracer at a headwater mountain stream using Markov-Chain Monte Carlo method to estimate model parameters and quantify uncertainty. Parameter estimation was exposed to a range of unsteady flow conditions through joint fitting of tracer data observed at different intervals of the base flow recession. This yielded a robust scaling of hyporheic parameters with time-varying streamflow which is evident from the good fit between modeled outputs and observations. The proposed approach enables Lagrangian-based modeling of solute transport under dynamic flow regimes, e.g., storm-affected flow where discharge inevitably changes over time. It also paves way for extending Lagrangian-based transport models to catchment and larger spatial scales.