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

Understanding how catchments store and release water of different ages has significant implications for flow and solute transport, as water ages encapsulate information about flow paths' characteristics

Model-based TTDs are subjected to uncertainty, which limits their ability with respect to decision support. In general, model prediction uncertainty stems from model inputs, structure, and parameters

A few studies have investigated the uncertainty in the estimated TTDs with SAS models.

Despite the studies cited above, there are other aspects that are particularly significant for SAS modeling and cause uncertainty in the simulated TTDs that have not yet been thoroughly investigated.
First, isotope data are generally sparse globally in space and time

This study bridges the aforementioned gaps by specifically exploring the combined effect of tracer data interpolation and model parameterizations on the simulated TTDs.
We investigated TTD uncertainty using an SAS-based catchment-scale transport model applied to the upper Selke catchment, Germany. We evaluated TTDs resulting from 12 model setups obtained by combining distinct interpolation techniques of

The upper Selke catchment is located in the Harz Mountains in Saxony-Anhalt, central Germany (Fig.

The upper Selke catchment, showing precipitation sampling points (purple dots), the river network (blue lines), and the elevation (in meters above sea level) as a colored map. The inset presents the location of the upper Selke catchment in Germany.

Daily hydroclimatic and monthly tracer data in the upper Selke catchment were available for the period between February 2013 and May 2015. Precipitation (

Data of

In this study, we used the

By definition, the TTD of streamflow

The isotopic signature in streamflow

In this study, we tested three SAS parameterizations: the power law time-invariant (PLTI; Eq.

The parameters

We tested the model with two spatial representation and two temporal interpolation methods for

SAS model results are sensitive to the choice of the temporal resolution of input tracer data, and a finer resolution is generally recommended to achieve a satisfactory level of detail

Predicted

In this study, different scenarios were used to quantify uncertainty in the modeled results. We tested 12 setups composed of three SAS functions (PLTI, PLTV, and BETATI), two temporal interpolations (step and sine function), and two spatial representations (raw and kriged values) of

List of model setups.

Model parameters and search ranges.

The informal likelihood of the Sequential Uncertainty Fitting

To assess the range of possible behavioral solutions and understand the level of uncertainty associated with it, we calculated the 95 % confidence interval (CI) derived by computing the 2.5 % and 97.5 % percentile values of the cumulative distribution in the parameters and time series of output variables

Modeled

Figure

Predicted

Despite the differences in the predicted

Box plots of model performance ranges in behavioral solutions. The letters on the

Ranges of the behavioral SAS parameters for the tested setups are summarized in Table S1 in the Supplement. Parameters for the SAS functions of

Figure

Predicted TT

Behavioral solutions obtained with PLTV revealed a similar pattern regardless of the interpolation employed (Fig.

In general, the variability in the predicted TT

SAS functions provided valuable insights into the catchment-scale water release dynamics. Figure

Percentage of behavioral solutions releasing water of different ages.

In this study, we characterized the TTD uncertainty arising from some significant and critical aspects for the SAS modeling. These aspects are also the most directly linked to the data interpolation and SAS parameterization that we explored in this work. The uncertainty analysis was carried out across the 12 tested setups corresponding to different combinations of spatiotemporal data interpolation techniques and SAS parameterizations.
Our results show that the uncertainty (i.e. 95 % CI) of the simulated TT

Uncertainty in the simulated TT

Likewise, the high-frequency reconstruction of

The spatial representation of

Finally, we found that the uncertainty was larger under dry conditions when lower flow and longer TT

The dissimilarities in the simulated TT

Our results provide visually plausible seasonal fluctuations in the predicted

First, the limited length of the

This study characterized the uncertainty in TTDs, which summarize the catchment's hydrologic transport behavior and, therefore, comprise decisive information for water managers. The value of TT

For example, knowing the TTD and its uncertainty may be crucial for characterizing the catchment's response to climatic change

Uncertainty in TTDs also impacts on assessing the fate of dissolved solutes, such as nitrates

Understanding the uncertainty in TTDs is crucial for the aforementioned implications. While previous studies have used only a specific SAS function and/or specific tracer data interpolation technique in time and space, here we show that there could be a wide range of different results in terms of water ages, model performance, and parameter uncertainty. This is due to the specific choice regarding SAS parameterization and tracer data interpolation. With this, we want to convey that uncertainty is omnipresent in TTD-based models, and we need to recognize it, especially when dealing with sparse tracer data and multiple choices for model parameterization. Therefore, we want to encourage future studies to explore these uncertainties in other catchments and different geophysical settings, with the final aim to investigate whether these uncertainties may affect the conclusions of water quantity and quality studies for management purposes.

This study explored the uncertainty in TTDs of streamflow, resulting from 12 model setups obtained from different SAS parameterizations (i.e. PLTI, PLTV, and BETATI), and reconstruction of the precipitation isotopic signature in time and space via interpolation (step function vs. sine fit and raw vs. kriged values).

We found satisfactory KGE values, whose differences across the tested setups were statistically significant, meaning that the choice of the setup matters. As a consequence, distinct setups led to considerably different simulated TT

These findings provide new insights into TTD uncertainty when high-frequency tracer data are missing and the SAS framework is used. Regardless of the degree of efficiency or uncertainty, the decision on which setup is more plausible depends on the best conceptual knowledge of the catchment functioning. We consider the presented approach to be potentially applicable to other studies to enable a better characterization of TTD uncertainty, improve TTD simulations and, ultimately, inform water management. These aspects are particularly crucial in view of increasingly extreme climatic conditions and worsening water pollution under global change.

The version of the model used in this study (v1.0) and its documentation are available at

The supplement related to this article is available online at:

AB conducted the model simulations, carried out the analysis, interpreted the results, and wrote the original draft of the paper. SRL and RK designed and conceptualized the study and provided data for model simulations. TVN provided technical support for modeling and helped organize the structure and content of the paper. AB, SRL, RK, and TVN conceived the methodology and experimental design. All co-authors helped AB interpret the results. All authors contributed to the review, final writing, and finalization of this work.

At least one of the (co-)authors is a member of the editorial board of

Publisher’s note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

The authors thank the Helmholtz Centre for Environmental Research – UFZ of the Helmholtz Association for funding this study; the German Weather Service and the mHM model team for providing the necessary input data; and the developers of the

The article processing charges for this open-access publication were covered by the Helmholtz Centre for Environmental Research – UFZ.

This paper was edited by Laurent Pfister and reviewed by Ciaran Harman and one anonymous referee.