scholarly journals Comment on “A comparison of catchment travel times and storage deduced from deuterium and tritium tracers using StorAge Selection functions” by Rodriguez et al. (2021)

2021 ◽  
Author(s):  
Michael Kilgour Stewart ◽  
Uwe Morgenstern ◽  
Ian Cartwright

Abstract. The combined use of deuterium and tritium to determine travel time distributions (TTDs) in streams is an important development in catchment hydrology (Rodriguez et al, 2021). This comment takes issue with Rodriguez et al.'s general rejection of the truncation hypothesis, i.e. that the almost exclusive use of stable isotopes has truncated our vision of streamflow TTDs and caused us to miss the long tails of old water often shown by tritium. We discuss reasons why this hypothesis may not hold for the catchment described by Rodriguez et al. (2021), but could still apply to a large proportion of all catchments. We also discuss more generally future applications of tritium in northern and southern hemisphere catchments.

2021 ◽  
Vol 25 (12) ◽  
pp. 6333-6338
Author(s):  
Michael Kilgour Stewart ◽  
Uwe Morgenstern ◽  
Ian Cartwright

Abstract. The combined use of deuterium and tritium to determine travel time distributions (TTDs) in streams is an important development in catchment hydrology (Rodriguez et al., 2021). This comment takes issue with Rodriguez et al.'s assertion that the truncation hypothesis may not hold for catchments in general, i.e. that the use of stable isotopes alone may not lead to underestimation of travel times or storage compared to tritium. We discuss reasons why the truncation hypothesis may not appear to hold for the catchment studied by Rodriguez et al. (2021) but could still apply to the majority of catchments. We also discuss more generally future applications of tritium in Northern Hemisphere and Southern Hemisphere catchments.


2021 ◽  
Vol 25 (1) ◽  
pp. 401-428
Author(s):  
Nicolas Björn Rodriguez ◽  
Laurent Pfister ◽  
Erwin Zehe ◽  
Julian Klaus

Abstract. Catchment travel time distributions (TTDs) are an efficient concept for summarizing the time-varying 3D transport of water and solutes towards an outlet in a single function of a water age and for estimating catchment storage by leveraging information contained in tracer data (e.g., deuterium 2H and tritium 3H). It is argued that the preferential use of the stable isotopes of O and H as tracers, compared to tritium, has truncated our vision of streamflow TTDs, meaning that the long tails of the distribution associated with old water tend to be neglected. However, the reasons for the truncation of the TTD tails are still obscured by methodological and data limitations. In this study, we went beyond these limitations and evaluated the differences between streamflow TTDs calculated using only deuterium (2H) or only tritium (3H). We also compared mobile catchment storage (derived from the TTDs) associated with each tracer. For this, we additionally constrained a model that successfully simulated high-frequency stream deuterium measurements with 24 stream tritium measurements over the same period (2015–2017). We used data from the forested headwater Weierbach catchment (42 ha) in Luxembourg. Time-varying streamflow TTDs were estimated by consistently using both tracers within a framework based on StorAge Selection (SAS) functions. We found similar TTDs and similar mobile storage between the 2H- and 3H-derived estimates, despite statistically significant differences for certain measures of TTDs and storage. The streamflow mean travel time was estimated at 2.90±0.54 years, using 2H, and 3.12±0.59 years, using 3H (mean ± 1 SD – standard deviation). Both tracers consistently suggested that less than 10 % of the stream water in the Weierbach catchment is older than 5 years. The travel time differences between the tracers were small compared to previous studies in other catchments, and contrary to prior expectations, we found that these differences were more pronounced for young water than for old water. The found differences could be explained by the calculation uncertainties and by a limited sampling frequency for tritium. We conclude that stable isotopes do not seem to systematically underestimate travel times or storage compared to tritium. Using both stable and radioactive isotopes of H as tracers reduced the travel time and storage calculation uncertainties. Tritium and stable isotopes both had the ability to reveal short travel times in streamflow. Using both tracers together better exploited the more specific information about longer travel times that 3H inherently contains due to its radioactive decay. The two tracers thus had different information contents overall. Tritium was slightly more informative than stable isotopes for travel time analysis, despite a lower number of tracer samples. In the future, it would be useful to similarly test the consistency of travel time estimates and the potential differences in travel time information contents between those tracers in catchments with other characteristics, or with a considerable fraction of stream water older than 5 years, since this could emphasize the role of the radioactive decay of tritium in discriminating younger water from older water.


2016 ◽  
Author(s):  
Falk Heße ◽  
Matthias Zink ◽  
Rohini Kumar ◽  
Luis Samaniego ◽  
Sabine Attinger

Abstract. Travel-time distributions are a comprehensive tool for the characterization of hydrological system dynamics. Unlike streamflow hydrographs, they describe the movement and storage of water inside and through the hydrological system. Until recently, studies using such travel-time distributions have generally either been applied to simple (artificial toy) models or to real-world catchments using available time series, e.g. stable isotopes. Whereas the former are limited in their realism, the latter are limited in their use of available data sets. In our study, we employ a middle ground by using the mesoscale Hydrological Model (mHM) and apply it to a catchment in Central Germany. Being able to draw on multiple large data sets for calibration and verification, we generate a large array of spatially distributed states and fluxes. These hydrological outputs are then used to compute the travel-time distributions for every grid cell in the modeling domain. A statistical analysis shows the general soundness of the upscaling scheme employed in mHM and reveal precipitation, saturated soil moisture and potential evapotranspiration as important predictors for explaining the spatial heterogeneity of mean travel times. In addition, we demonstrate and discuss the high information content of mean travel times for characterization of internal hydrological processes.


2020 ◽  
Author(s):  
Julian Klaus ◽  
Nicolas Rodriguez ◽  
Laurent Pfister ◽  
Erwin Zehe

<p>Catchment travel time distributions (TTDs) are an integrative measure of time-varying flow paths and hydrological processes, commonly derived from tracer data (e.g. 2-H, 3-H). Recently, it has been argued that the use of stable isotopes of O and H compared to tritium neglects the long tails of TTDs and thus truncates our vision on streamflow age. However, the reasons for the truncation of the TTD remain obscured by methodological and data limitations, including different mathematical models and sampling strategies. In this study, we apply composite SAS functions to a forested headwater catchment in Luxembourg, where the complexity of streamflow generation leads to flow paths with highly different TTDs. We calibrate the model with high-frequency (sub-daily) deuterium measurements, as well as nearly 30 tritium stream samples collected over a two-year period. We simulated TTDs based on each tracer individually and jointly. We found that, when using the two tracers in a coherent methodological framework, both tracers result in similar TTD and storage for the studied catchment. We found small differences in the TTDs that might be explained by calculation uncertainties, as well as by the limited sampling frequency for tritium. Using both stable and radioactive isotopes of H as tracers reduced uncertainties in the water age and storage calculations. While tritium and stable isotopes delivered redundant information about younger water, the use of both tracers leveraged the more specific information content of tritium on longer ages in the system. The two tracers had overall different information contents. We found that 30 tritium samples contained more bits of information than approximately 1000 deuterium samples, underlying the importance of complementing stable isotopes studies with tritium data.</p>


2019 ◽  
Author(s):  
Nicolas B. Rodriguez ◽  
Laurent Pfister ◽  
Erwin Zehe ◽  
Julian Klaus

Abstract. Catchment travel time distributions (TTDs) are an efficient concept to summarize the time-varying 3-dimensional transport of water and solutes to an outlet in a single function of water age and to estimate catchment storage by leveraging information contained in tracer data (e.g. 2H and 3H). It is argued that the increasing use of the stable isotopes of O and H compared to tritium as tracers has truncated our vision of streamflow TTDs, meaning that the long tails associated with old water are neglected. However, the reasons for the truncation of the TTD tails are still obscured by methodological and data limitations. In this study, we went beyond these limitations and tested the hypothesis that streamflow TTDs calculated using only deuterium (2H) or only tritium (3H) are different. We similarly tested if the mobile catchment storage (derived from the TTDs) associated with each tracer is different. For this we additionally constrained a model successfully developed to simulate high-frequency stream deuterium measurements with about 30 stream tritium measurements over the same period (2015–2017). We used data from the forested headwater Weierbach catchment (42 ha) in Luxembourg. The streamflow TTDs were estimated in unsteady conditions by using both tracers coherently within a framework based on StorAge Selection (SAS) functions. We found equal TTDs and equal mobile storage between the 2H- and 3H-derived estimates. The truncation hypothesis was thus rejected. The small differences we found could be explained by the calculation uncertainties and by a limited sampling frequency for tritium. Using both stable and radioactive isotopes of H as tracers reduced the age and storage uncertainties. Although tritium and stable isotopes had redundant information about younger water, using both tracers better exploited the more specific information about longer ages that 3H inherently contains, and it could be even better in the next decades. The two tracers thus had overall different information contents. Tritium was however slightly more informative and cost-effective than stable isotopes for travel time analysis. We thus reiterate the call of Stewart et al. (2012) to measure tritium in the streams for travel time analysis, and emphasize the need for high-frequency tritium sampling in future studies to match the resolution in stable isotopes.


2021 ◽  
Vol 6 (1) ◽  
pp. e004318
Author(s):  
Aduragbemi Banke-Thomas ◽  
Kerry L M Wong ◽  
Francis Ifeanyi Ayomoh ◽  
Rokibat Olabisi Giwa-Ayedun ◽  
Lenka Benova

BackgroundTravel time to comprehensive emergency obstetric care (CEmOC) facilities in low-resource settings is commonly estimated using modelling approaches. Our objective was to derive and compare estimates of travel time to reach CEmOC in an African megacity using models and web-based platforms against actual replication of travel.MethodsWe extracted data from patient files of all 732 pregnant women who presented in emergency in the four publicly owned tertiary CEmOC facilities in Lagos, Nigeria, between August 2018 and August 2019. For a systematically selected subsample of 385, we estimated travel time from their homes to the facility using the cost-friction surface approach, Open Source Routing Machine (OSRM) and Google Maps, and compared them to travel time by two independent drivers replicating women’s journeys. We estimated the percentage of women who reached the facilities within 60 and 120 min.ResultsThe median travel time for 385 women from the cost-friction surface approach, OSRM and Google Maps was 5, 11 and 40 min, respectively. The median actual drive time was 50–52 min. The mean errors were >45 min for the cost-friction surface approach and OSRM, and 14 min for Google Maps. The smallest differences between replicated and estimated travel times were seen for night-time journeys at weekends; largest errors were found for night-time journeys at weekdays and journeys above 120 min. Modelled estimates indicated that all participants were within 60 min of the destination CEmOC facility, yet journey replication showed that only 57% were, and 92% were within 120 min.ConclusionsExisting modelling methods underestimate actual travel time in low-resource megacities. Significant gaps in geographical access to life-saving health services like CEmOC must be urgently addressed, including in urban areas. Leveraging tools that generate ‘closer-to-reality’ estimates will be vital for service planning if universal health coverage targets are to be realised by 2030.


Author(s):  
Monika Filipovska ◽  
Hani S. Mahmassani ◽  
Archak Mittal

Transportation research has increasingly focused on the modeling of travel time uncertainty in transportation networks. From a user’s perspective, the performance of the network is experienced at the level of a path, and, as such, knowledge of variability of travel times along paths contemplated by the user is necessary. This paper focuses on developing approaches for the estimation of path travel time distributions in stochastic time-varying networks so as to capture generalized correlations between link travel times. Specifically, the goal is to develop methods to estimate path travel time distributions for any path in the networks by synthesizing available trajectory data from various portions of the path, and this paper addresses that problem in a two-fold manner. Firstly, a Monte Carlo simulation (MCS)-based approach is presented for the convolution of time-varying random variables with general correlation structures and distribution shapes. Secondly, a combinatorial data-mining approach is developed, which aims to utilize sparse trajectory data for the estimation of path travel time distributions by implicitly capturing the complex correlation structure in the network travel times. Numerical results indicate that the MCS approach allowing for time-dependence and a time-varying correlation structure outperforms other approaches, and that its performance is robust with respect to different path travel time distributions. Additionally, using the path segmentations from the segment search approach with a MCS approach with time-dependence also produces accurate and robust estimates of the path travel time distributions with the added benefit of shorter computation times.


2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Cong Bai ◽  
Zhong-Ren Peng ◽  
Qing-Chang Lu ◽  
Jian Sun

Accurate and real-time travel time information for buses can help passengers better plan their trips and minimize waiting times. A dynamic travel time prediction model for buses addressing the cases on road with multiple bus routes is proposed in this paper, based on support vector machines (SVMs) and Kalman filtering-based algorithm. In the proposed model, the well-trained SVM model predicts the baseline bus travel times from the historical bus trip data; the Kalman filtering-based dynamic algorithm can adjust bus travel times with the latest bus operation information and the estimated baseline travel times. The performance of the proposed dynamic model is validated with the real-world data on road with multiple bus routes in Shenzhen, China. The results show that the proposed dynamic model is feasible and applicable for bus travel time prediction and has the best prediction performance among all the five models proposed in the study in terms of prediction accuracy on road with multiple bus routes.


1977 ◽  
Vol 67 (1) ◽  
pp. 33-42
Author(s):  
Mark E. Odegard ◽  
Gerard J. Fryer

Abstract Equations are presented which permit the calculation of distances, travel times and intensity ratios of seismic rays propagating through a spherical body with concentric layers having velocities which vary linearly with radius. In addition, a method is described which removes the infinite singularities in amplitude generated by second-order discontinuities in the velocity profile. Numerical calculations involving a reasonable upper mantle model show that the standard deviations of the errors for distance, travel time and intensity ratio are 0.0046°, 0.057 sec, and 0.04 dB, respectively. Computation time is short.


1952 ◽  
Vol 42 (4) ◽  
pp. 313-314
Author(s):  
V. C. Stechschulte

Abstract A simple method is outlined for obtaining from a time-distance curve of a deep-focus earthquake a table of travel times within an earth “stripped” to the depth h, the depth of focus. The method depends on the fact that such a curve for a deep-focus earthquake has a point of inflection and therefore has the same slope at two different values of epicentral distance. The Herglotz-Wiechert method may then be applied to these travel times to obtain a velocity-depth distribution.


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