Time-variable transit time distributions (TTDs) have been utilized as a tool to understand how catchments transmit water. However, most of the existing TTD estimation methods require to impose certain structures on those TTDs a priori, which could lead to misinterpreting data. Kim and Troch (2020) present a data-based method to estimate time-variable TTDs without imposing their structure a priori. The core of the method is the use of a revised flow-weighted time, where TTDs do not reflect variable external forcings directly. The functional forms of the TTDs are much simpler in flow-weighted time, compared to those in calendar time, and this allows for easier estimation of TTDs. Dynamic (state-dependent) multiple linear regression methods were applied to estimate the time-variable TTDs in flow-weighted time, which can eventually be transformed back to calendar time. The method performs well in a proof-of-concept demonstration with synthetic data sets.
At LEO, we have recently completed so-called Random Forcing experiments. The experiments involve raining on the three hillslopes simultaneously with random intensity and duration, as well as with random Deuterium concentrations of the rain water. The data are currently being analyzed to test the method of Kim and Troch. This work is part of an NSF funded project "Collaborative Research: Developing Concentration - Ratio - Discharge (C-R-Q) relationships to disentangle weathering signatures of the Critical Zone".