Transit Time Distributions Estimation Exploiting Flow-Weighted Time: Theory and Proof-of-Concept

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. We 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. We also discuss potential generalizations of the proposed method.