Spatially integrated transport models have been applied widely to model hydrologic transport. However, we lack simple and process‐based theoretical tools to predict the transport closures—transit time distributions (TTDs) and StorAge Selection (SAS) functions. This limits our ability to infer characteristics of hydrologic systems from tracer observations and to make first‐order estimates of SAS functions in catchments where no tracer data is available. Here we present a theoretical framework linking TTDs and SAS functions to hydraulic groundwater theory at the hillslope scale. For hillslopes where the saturated hydraulic conductivity declines exponentially with depth, analytical solutions for the closures are derived that can be used as hypotheses to test against data. In the simplest form, the hillslope SAS function resembles a uniform or exponential distribution (corresponding to flow pathways in the saturated zone) offset from zero by the storage in the unsaturated zone that does not contribute to discharge. The framework is validated against nine idealized virtual hillslopes constructed using a 2‐D Richards equation‐based model, and against data from tracer experiments in two artificial hillslopes. Modeled internal age, life expectancy, and transit time structures reproduce theoretical predictions. The experimental data also support the theory, though further work is needed to account for the effects of time‐variability. The shape and tailing of TTDs and their power spectra are discussed. The theoretical framework yields several dimensionless numbers that can be used to classify hillslope scale flow and transport dynamics and suggests distinct water age structures for high or low Hillslope number.
Accurately quantifying and predicting the reactive transport of nitrate () in hydrologic systems continues to be a challenge, due to the complex hydrological and biogeochemical interactions that underlie this transport. Recent advances related to time‐variant water age have led to a new method that probes water mixing and selection behaviors using StorAge Selection (SAS) functions. In this study, SAS functions were applied to investigate storage, water selection behaviors, and export regimes in a tile‐drained corn‐soybean field. The natural abundance stable nitrogen and oxygen isotopes of tile drainage were also measured to provide constraints on biogeochemical transformations. The SAS functions, calibrated using chloride measurements at tile drain outlets, revealed a strong young water preference during tile discharge generation. The use of a time‐variant SAS function for tile discharge generated unique water age dynamics that reveal an inverse storage effect driven by the activation of preferential flow paths and mechanically explain the observed variations in isotopes. Combining the water age estimates with isotope fingerprinting shed new light on export dynamics at the tile‐drain scale, where a large mixing volume and the lack of a strong vertical contrast in concentration resulted in chemostatic export regimes. For the first time, isotopes were embedded into a water age‐based transport model to model reactive transport under transient conditions. The results of this modeling study provided a proof‐of‐concept for the potential of coupling water age modeling with isotope analysis to elucidate the mechanisms driving reactive transport.
more » « less- NSF-PAR ID:
- 10480482
- Publisher / Repository:
- DOI PREFIX: 10.1029
- Date Published:
- Journal Name:
- Water Resources Research
- Volume:
- 59
- Issue:
- 12
- ISSN:
- 0043-1397
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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