Numerical evaluation of the PERTH (PERiodic Tracer Hierarchy) method for estimating time-variable travel time distribution in variably saturated soils

The distribution of water travel times is one of the crucial hydrologic characteristics of the catchment. Recently, it has been argued that a rigorous treatment of travel time distributions should allow for their variability in time because of the variable fluxes and partitioning of water in the water balance, and the consequent variable storage of a catchment. We would like to be able to observe the structure of the temporal variations in travel time distributions under controlled conditions, such as in a soil column or under irrigation experiments. However, time-variable travel time distributions are difficult to observe using typical active and passive tracer approaches. Time-variability implies that tracers introduced at different times will have different travel time distributions. The distribution may also vary during injection periods. Moreover, repeat application of a single tracer in a system with significant memory leads to overprinting of break-through curves, which makes it difficult to extract the original break-through curves, and the number of ideal tracers that can be applied is usually limited. Recognizing these difficulties, the PERTH (PERiodic Tracer Hierarchy) method has been developed. The method provides a way to estimate time-variable travel time distributions by tracer experiments under controlled conditions by employing a multi-tracer hierarchy under periodical hydrologic forcing inputs. The key assumption of the PERTH method is that as time gets sufficiently large relative to injection time, the average travel time distribution of two distinct ideal tracers injected during overlapping periods become approximately equal. Thus one can be used as a proxy for the other, and the breakthrough curves of tracers applied at different times in a periodic forcing condition can be separated from one another. In this study, we tested the PERTH method numerically for the case of infiltration at the plot scale using HYDRUS-1D and a particle-tracking model. HYDRUS-1D was used to solve Richards' equation and the advection-dispersion equation for ideal tracers introduced at different points during an irrigation event in a ';virtual experiment', and the PERTH method was used to extract the time-variable transit time distribution. The 1D particle-tracking model was developed to simulate particle trajectories using the Fokker-Plank-Ito scheme based on the saturation and water flux fields estimated by HYDRUS-1D. The results of the particle-tracking model estimate the ';true' travel time distribution and allow us to validate the result of PERTH. The result reveals that the PERTH method well approximates the simulated time-variable travel time distribution on plot scale. Also, the key assumption of PERTH method was supported in this case. In addition, this research further suggests an optimal way to configure the tracer hierarchy of PERTH in complex flow experiments. The numerical analysis of this study demonstrates that the PERTH method may be a useful method for obtaining experimental observations of time-variable travel time distributions in well-controlled environments where periodic forcing conditions can be set.