Using Information Theory to Optimize Sampling of Isotope Tracers for Transit Time Estimation

Tracer-based approaches play a crucial role in advancing our understanding of hydrological processes, particularly in determining catchment transit time distributions (TTDs). TTDs describe the distribution of water ages in fluxes leaving a catchment, providing critical insights into flow paths, storage, and transformation processes. Despite the value of these analyses, applying tracer-based methods often remains challenging due to the high costs and practical difficulties associated with comprehensive sampling strategies. Multi-tracer approaches are particularly valuable because different tracers (e.g., stable isotopes and tritium) provide additional information of catchment transit times, enabling more comprehensive system characterization. In this presentation, we present a methodological approach to assess the optimization of sampling strategies for tracer-based TTD modeling using isotopic data and the SAS (StorAge Selection) framework trough an information-theoretic approach. In this context, sampling design refers to the systematic evaluation of the informational contribution of individual samples and their combinations in estimating transit time distributions (TTDs). Specifically, we quantify the information content of individual tracer samples, assess how different combinations of samples collectively enhance the accuracy of TTD estimations, and evaluate and present the effectiveness of different sampling strategies. Additionally, we compare the information content of different tracers (e.g., deuterium and tritium) with SAS-based transit time models and evaluate how each tracer improves the precision of TTD predictions. The tested sampling strategies included baseline and event-based strategies. Our approach builds on recent advancements in hydrological theory, including the use of multi-tracer methods and the SAS framework. The results will provide a detailed comparison of the information content of different samples, tracers, and sampling designs, highlighting the relative contribution of deuterium and tritium to inform TTD analysis. The results from this study will contribute to informing hydrological field campaigns by providing guidelines on optimal sampling strategies for TTDs estimation. By that, guidelines for optimal sampling protocols for information gain balanced with cost for field work can be developed in the future. The findings will promote the broader application of tracer-based methods in hydrology, offering practical solutions for data-scarce environments and enhancing sustainable water management practices.