A comparison of Lumped Convolution approach and Ensemble Hydrograph Separation in soil transit time distribution estimations: case study of San Francisco catchment

Mean Transit Time (MTT) and Transit time distribution (TTD) functions are crucial for understanding the temporal dynamics of water flow through a catchment system, particularly in the context of rainfall-runoff processes that govern the solute storage and transport. Traditionally, these insights have been assessed using lumped TTD functions through models based on quasi-linearity and steady-state conditions. 
In contrast, the Ensemble Hydrograph Separation technique (EHS) presents a promising alternative for estimating TTD through multiple linear equations representing the relation between tracer fluctuations. This approach is advantageous, eliminating the need for continuous time series data of tracer measures and avoiding constraints related to the shape of transit distributions or system stationarity. However, EHS faces a sensitivity challenge in its regularization process, governed by a parameter denoted as "v," making the technique susceptible to either under-smoothing or over-smoothing the TTD function. Consequently, the judicious estimation of the regularization parameter within EHS becomes imperative.
This study aims to investigate how both the traditional lumped TTD approach and the innovative EHS method contribute to our understanding of catchment hydrology. The present investigation was conducted using stable water isotope data of stream and soil water collected in a typical Andean tropical mountain cloud forest catchment. The sampling was conducted at six sites along two altitudinal transects (at elevations of 3000 m, 2000 m, and 1000 m), encompassing two distinct land covers (forest and pasture). At each site, soil water samples were collected at three different depths (0.10, 0.25, and 0.40 m below ground). The main objective is to assess the feasibility of substituting one method with the alternative by comparing their performance using different evaluation criteria such as the Nash-Sutcliffe coefficient (NSE), mean absolute error (MAE), and coefficient of determination (R²).
Through Monte-Carlo simulations, we calibrated the “v” parameter and conducted a comprehensive comparison of both approaches. At 75% of the monitoring points, we observed NSE and R² coefficients exceeding 0.65. These results align with previous studies, emphasizing the feasibility of assuming stationary conditions in humid tropical ecosystems. The study systematically examined the concordance between the Lumped TTD approach and Ensemble Hydrograph Separation (EHS) findings when utilizing similar TTDs. Furthermore, it provided a detailed analysis of the strengths and limitations of EHS implementation with actual real data. The insights gained from this research can be extrapolated to identify situations where each approach may be more suitable, offering valuable recommendations for their future application in various catchments.