This study is driven by the question of how quickly a solute will be flushed from an aquatic system after input of the solute into the system ceases. Simulating the fate and transport of a solute in an aquatic system can be performed at high spatial and temporal resolution using a computationally demanding state-of-the-art hydrodynamics simulator. However, uncertainties in the system often require stochastic treatment and risk-based analysis requires a large number of simulations rendering the use of a physical model impractical. A surrogate model that represents a second-level physical abstraction of the system is developed and coupled with a Monte Carlo based method to generate volumetric inflow scenarios. The surrogate model provides an approximate 8 orders of magnitude speed-up over the full physical model enabling uncertainty quantification through Monte Carlo simulation. The approach developed here consists of an stochastic inflow generator, a solute concentration prediction mechanism based on the surrogate model, and a system response risk assessment method. The probabilistic outcome provided relates the uncertain quantities to the relevant response in terms of the system’s ability to remove the solute. We develop a general approach that can be applied in a generality of system configurations and types of solute. As a test case, we present a study specific to salinization of a lake.