Bayesian hydrograph separation in a minimally gauged alpine volcanic watershed in central Chile

Abstract

This study examines the question of how much information one can extract from a tracer-based hydrograph separation in a remote and minimally gaged alpine catchment in Chile. We combine PCA-based endmember mixing analysis to identify the sources of flow contribution to the Diguillín River with a hierarchical Bayesian mixing model to integrate spatial and temporal variability in endmember concentration and quantify the source contributions to streamflow over time. The PCA-analysis shows that precipitation isotopes do not vary by elevation (e.g. snow and rainfall had identical signatures) but vary significantly by season, and that a third endmember is necessary to bound streamflow variability at the basin outlet, which was not captured by our field sampling. One of the main advantages of Bayesian methods is the quasi-machine learning capabilities, where we treated the third endmember as a parameter from which the mixing model could both estimate proportional contributions as well as posterior estimates for the tracer concentrations. The two tracer, three endmember hydrograph separation revealed groundwater to be the largest and precipitation (rain and snow) to be the smallest contributor, on average, to streamflow with the third unknown endmember contributing around 40% of streamflow during the Winter wet season. We hypothesize that interflow is occurring as the third endmember in the Alto Diguillín subwatershed, based on inferred tracer values and the presence of alluvium atop impermeable bedrock along certain reaches. More work is necessary to observe and sample these flowpaths, which was not possible during this study. The results of this work have implications for water resource management, since groundwater sustains the majority of streamflow in the Diguillín, and climate change will impact the timing and quantity of baseflow and interflow. Overall, we demonstrate the utility of combining PCA with Bayesian statistical modeling and inference to extract maximum information from a limited field dataset in a remote alpine catchment. The findings of this work can guide future water management in the Diguillín, but also provide clear questions for future research.

Where Is the Bottom of a Watershed?

“…Across larger river basins, Schaller and Fan () and Fan () challenged the commonly held view that catchments are closed systems, finding instead that many are regional groundwater importers or exporters. Similarly, multiple CZOs and other experimental sites operating at headwater scales have found that groundwater in fractured bedrock aquifers commonly contributes to streamflow (Brantley et al, ; Jin et al, ; Markovich, Dahlke, et al, ; McIntosh et al, ; Payn et al, ; White et al, ). Key to this discussion is the recent recognition that even at well‐studied sites, we are only beginning to detect that our “shallow views” on the hydrologic cycle may miss large fluxes of water or oversimplify our conceptual models of these systems.…”

Uncertainties in measuring and estimating water‐budget components: Current state of the science

“…Posterior distributions for contributing stream components are estimated through Monte Carlo methods, where uncertainty is presented as confidence intervals corresponding to the 5th and 95th percentiles of the distribution. Bayesian approaches are also useful at ungaged stream locations (Markovich et al, 2019). He et al (2020) estimated the uncertainty of the fractional proportion of groundwater in streamflow using EMMA (standard deviation from 12% to 15%) and Bayesian approaches (standard deviations from 1% to 12%).…”

Estimation of the E/I ratio in Aquatic Systems: A Bayesian Approach in the Craig-Gordon Model

“…This full distribution encapsulates information from the observed data through the likelihood, and our prior beliefs through the priors. We attained this by utilizing the No-U-Turn Sampler (NUTS), a variant of the Hamiltonian Monte Carlo (HMC) algorithm [41,42]. The application of NUTS algorithm was executed in PyMC3 [43], where we initiated four chains for each parameter, generating 5000 samples per chain following a tuning period of 1000 iterations.…”