Uncertainty in water transit time estimation with StorAge Selection functions and tracer data interpolation

Transit time distributions (TTDs) of streamflow are useful descriptors for understanding flow and solute transport in catchments. Catchment-scale TTDs can be modeled using tracer data (e.g. oxygen isotopes, such as δ18O) in inflow and outflows by employing StorAge Selection (SAS) functions. However, tracer data are often sparse in space and time, so they need to be interpolated to increase their spatiotemporal resolution. Moreover, SAS functions can be parameterized with different forms, but there is no general agreement on which one should be used. Both of these aspects induce uncertainty in the simulated TTDs, and the individual uncertainty sources as well as their combined effect have not been fully investigated. This study provides a comprehensive analysis of the TTD uncertainty resulting from 12 model setups obtained by combining different interpolation schemes for δ18O in precipitation and distinct SAS functions. For each model setup, we found behavioral solutions with satisfactory model performance for in-stream δ18O (KGEĝ€¯>ĝ€¯0.55, where KGE refers to the Kling-Gupta efficiency). Differences in KGE values were statistically significant, thereby showing the relevance of the chosen setup for simulating TTDs. We found a large uncertainty in the simulated TTDs, represented by a large range of variability in the 95ĝ€¯% confidence interval of the median transit time, varying at the most by between 259 and 1009ĝ€¯d across all tested setups. Uncertainty in TTDs was mainly associated with the temporal interpolation of δ18O in precipitation, the choice between time-variant and time-invariant SAS functions, flow conditions, and the use of nonspatially interpolated δ18O in precipitation. We discuss the implications of these results for the SAS framework, uncertainty characterization in TTD-based models, and the influence of the uncertainty for water quality and quantity studies

Evaluating the added value of young water fractions for determining water transit times in diverse catchments

Water transit time distributions (TTDs) are important descriptors of hydrological functioning and solute mobilization in catchments. The use of transport models based on StorAge Selection (SAS) functions is promising for characterizing non-stationary TTDs. Model parameters are typically calibrated using tracer concentration in inflow (e.g., precipitation) and outflow (e.g., streamflow) in order to obtain suitable values of SAS function parameters and, thereby, simulate TTDs at catchment-scale. However, due to uncertainties in tracer data and equifinality problems in SAS modelling, modeled TTDs can be subject to considerable uncertainty. Therefore, we need alternative and independent methods that can help constrain model parameters. An example is the young water fraction (Fyw), which quantifies the proportion of catchment outflow younger than approximately 2–3 months. Our work attempts to explore the robustness of Fyw in constraining SAS model parameter values and, in turn, reducing predictive uncertainty of TTDs in multiple contrasting sub-catchments in the Central European Bode River Basin. We simulated TTDs using sparse (i.e., monthly) stable water isotope data (δ¹⁸O) in streamflow for calibration in an experimental SAS modelling framework. In a subsequent step, we directly compared the model estimates of long-term average (marginal) TTDs with Fyw derived from the seasonal cycles of δ¹⁸O measured in precipitation and streamflow. Our results showcase if and to what extent Fyw is a valuable additional constraint to infer SAS parametrizations as well as improve TTD predictions and the characterization of water age selection dynamics, and identify potentials and gaps in isotope-based TTD models. Our results also show how the effectiveness of Fyw in reducing the predictive uncertainty of TTDs may depend on the water use by plants and land use change across physiographically different sub-catchments. Overall, as the relevance of Fyw in TTD modeling is not yet well established, our aim is to investigate whether additional indicators such as Fyw are useful for TTD modeling and thus allow improving the description of flow and transport in catchment areas, especially in situations where a high-resolution tracer data are lacking

Investigating the value of regional water isotope data on transit time and SAS modelling

High nutrient concentrations despite mitigation measures and reduced inputs are a common problem in anthropogenically impacted catchments. To investigate how water and solutes of different ages are mixed and released from catchment storage to the stream, catchment-scale models based on water transit time from StorAge Selection functions (SAS) are a promising tool. Tracking fluxes of environmental tracers, such as stable water isotopes, allows to calibrate and validate these models. However, this requires collection of water samples with an adequate temporal and spatial resolution, while sampling in catchments at the management scale is often limited by the high costs of the instruments, maintenance and chemical analysis. Therefore, temporal and spatial interpolation techniques are needed. This study demonstrates how to deal with sparse tracer data in space and time, and evaluates if these data are valuable to constrain the subsurface mixing dynamics and transit time with SAS modelling. We simulated water isotope data in diverse sub-basins of the Bode catchment (Germany) and calibrated the SAS function parameters against the measured streamflow isotope data. We tested four different combinations of spatial and temporal interpolation of the measured precipitation isotope data. In terms of temporal interpolation, monthly oxygen isotopes in precipitation (δ18OP) collected between 2012 and 2015 were converted to a daily time step with a step function and sinusoidal interpolation. In terms of spatial interpolation, the model was tested with raw values of δ18OP collected at a specific sampling point and with δ18OP interpolated using kriging to gain the spatial pattern of precipitation. The effect of the spatial and temporal interpolation techniques on the modeled SAS functions was analyzed using different parameterizations of the SAS function (i.e., power law time-invariant, power law time-variant and beta law). The results show how tracer input data with different distribution in time and space affect the SAS parameterization and water transit time. Moreover, they reveal preference of the sub-basins to mobilize either younger or older water, which has implications on how water flows through a catchment and on the fate of solutes

Investigating the value of regional water isotope data on transit time and SAS modelling

High nutrient concentrations despite mitigation measures and reduced inputs are a common problem in anthropogenically impacted catchments. To investigate how water and solutes of different ages are mixed and released from catchment storage to the stream, catchment-scale models based on water transit time from StorAge Selection functions (SAS) are a promising tool. Tracking fluxes of environmental tracers, such as stable water isotopes, allows to calibrate and validate these models. However, this requires collection of water samples with an adequate temporal and spatial resolution, while sampling in catchments at the management scale is often limited by the high costs of the instruments, maintenance and chemical analysis. Therefore, temporal and spatial interpolation techniques are needed. This study demonstrates how to deal with sparse tracer data in space and time, and evaluates if these data are valuable to constrain the subsurface mixing dynamics and transit time with SAS modelling. We simulated water isotope data in diverse sub-basins of the Bode catchment (Germany) and calibrated the SAS function parameters against the measured streamflow isotope data. We tested four different combinations of spatial and temporal interpolation of the measured precipitation isotope data. In terms of temporal interpolation, monthly oxygen isotopes in precipitation (δ18OP) collected between 2012 and 2015 were converted to a daily time step with a step function and sinusoidal interpolation. In terms of spatial interpolation, the model was tested with raw values of δ18OP collected at a specific sampling point and with δ18OP interpolated using kriging to gain the spatial pattern of precipitation. The effect of the spatial and temporal interpolation techniques on the modeled SAS functions was analyzed using different parameterizations of the SAS function (i.e., power law time-invariant, power law time-variant and beta law). The results show how tracer input data with different distribution in time and space affect the SAS parameterization and water transit time. Moreover, they reveal preference of the sub-basins to mobilize either younger or older water, which has implications on how water flows through a catchment and on the fate of solutes

Evaluating the added value of young water fractions for determining water transit times in diverse catchments

Water transit time distributions (TTDs) are important descriptors of hydrological functioning and solute mobilization in catchments. The use of transport models based on StorAge Selection (SAS) functions is promising for characterizing non-stationary TTDs. Model parameters are typically calibrated using tracer concentration in inflow (e.g., precipitation) and outflow (e.g., streamflow) in order to obtain suitable values of SAS function parameters and, thereby, simulate TTDs at catchment-scale. However, due to uncertainties in tracer data and equifinality problems in SAS modelling, modeled TTDs can be subject to considerable uncertainty. Therefore, we need alternative and independent methods that can help constrain model parameters. An example is the young water fraction (Fyw), which quantifies the proportion of catchment outflow younger than approximately 2–3 months. Our work attempts to explore the robustness of Fyw in constraining SAS model parameter values and, in turn, reducing predictive uncertainty of TTDs in multiple contrasting sub-catchments in the Central European Bode River Basin. We simulated TTDs using sparse (i.e., monthly) stable water isotope data (δ¹⁸O) in streamflow for calibration in an experimental SAS modelling framework. In a subsequent step, we directly compared the model estimates of long-term average (marginal) TTDs with Fyw derived from the seasonal cycles of δ¹⁸O measured in precipitation and streamflow. Our results showcase if and to what extent Fyw is a valuable additional constraint to infer SAS parametrizations as well as improve TTD predictions and the characterization of water age selection dynamics, and identify potentials and gaps in isotope-based TTD models. Our results also show how the effectiveness of Fyw in reducing the predictive uncertainty of TTDs may depend on the water use by plants and land use change across physiographically different sub-catchments. Overall, as the relevance of Fyw in TTD modeling is not yet well established, our aim is to investigate whether additional indicators such as Fyw are useful for TTD modeling and thus allow improving the description of flow and transport in catchment areas, especially in situations where a high-resolution tracer data are lacking