scholarly journals The Wavelets show it – the transit time of water varies in time

2018 ◽  
Vol 66 (3) ◽  
pp. 295-302 ◽  
Author(s):  
Milan Onderka ◽  
Vladimír Chudoba
Keyword(s):  
Transit Time ◽  
Time Distribution ◽  
Conceptual Modeling ◽  
Flow Paths ◽  
Transit Times ◽  
The Mean ◽  
Transit Time Distribution ◽  
Mathematical Techniques ◽  
Time Invariant

Abstract The ways how water from rain or melting snow flows over and beneath the Earth‘s surface affects the timing and intensity at which the same water leaves a catchment. Several mathematical techniques have been proposed to quantify the transit times of water by e.g. convolving the input-output tracer signals, or constructing frequency response functions. The primary assumption of these techniques is that the transit time is regarded time-invariant, i.e. it does not vary with temporarily changing e.g. soil saturation, evaporation, storage volume, climate or land use. This raises questions about how the variability of water transit time can be detected, visualized and analyzed. In this paper we present a case study to show that the transit time is a temporarily dynamic variable. Using a real-world example from the Lower Hafren catchment, Wales, UK, and applying the Continuous Wavelet Transform we show that the transit time distributions are time-variant and change with streamflow. We define the Instantaneous Transit Time Distributions as a basis for the Master Transit Time Distribution. We show that during periods of elevated runoff the transit times are exponentially distributed. A bell-shaped distribution of travel times was observed during times of lower runoff. This finding is consistent with previous investigations based on mechanistic and conceptual modeling in the study area according to which the diversity of water flow-paths during wet periods is attributable to contributing areas that shrink and expand depending on the duration of rainfall. The presented approach makes no assumptions about the shape of the transit time distribution. The mean travel time estimated from the Master Transit Time Distribution was ~54.3 weeks.

scholarly journals Study of capillary transit time distribution in coherent hemodynamics spectroscopy

2015 ◽  
Vol 08 (02) ◽  
pp. 1550025 ◽  
Author(s):  
Angelo Sassaroli ◽  
Jana Kainerstorfer ◽  
Sergio Fantini
Keyword(s):  
Blood Flow ◽  
Transit Time ◽  
Time Distribution ◽  
Mean Value ◽  
Original Model ◽  
Extended Model ◽  
Transit Times ◽  
Sinusoidal Input ◽  
The Mean ◽  
Transit Time Distribution

A recently proposed analytical hemodynamic model1 [S. Fantini, NeuroImage85, 202–221 (2014)] is able to predict the changes of oxy, deoxy, and total hemoglobin concentrations (model outputs) given arbitrary changes in blood flow, blood volume, and rate of oxygen consumption (model inputs). One assumption of this model is that the capillary compartment is characterized by a single blood transit time. In this work, we have extended the original model by considering a distribution of capillary transit times and we have compared the outputs of both models (original and extended) for the case of sinusoidal input signals at different frequencies, which realizes the new technique of coherent hemodynamics spectroscopy (CHS). For the calculations with the original model, we have used the mean value of the distribution of capillary transit times considered in the extended model. We have found that, for distributions of capillary transit times having mean values around 1 s and a standard deviation less than about 45% of the mean value, the original and extended models yield the same CHS spectra (i.e., model outputs versus frequency of oscillation) within typical experimental errors. For wider capillary transit time distributions, the two models yield different CHS spectra. By assuming that Poiseuille's law is valid in the capillary compartment, we have related the distribution of capillary transit times to the distributions of capillary lengths and capillary speed of blood flow to calculate the average capillary and venous saturations. We have found that, for standard deviations of the capillary transit time distribution that are less than about 80% of the mean value, the average capillary saturation is always larger than the venous saturation. By contrast, the average capillary saturation may be less than the venous saturation for wider distributions of the capillary transit times.

Morphological controls on groundwater residence times of shallow aquifers

2020 ◽  
Author(s):  
Alexandre Gauvain ◽  
Sarah Leray ◽  
Jean Marçais ◽  
Camille Vautier ◽  
Luc Aquilina ◽  
...  
Keyword(s):  
Standard Deviation ◽  
Transit Time ◽  
Time Distribution ◽  
Residence Times ◽  
Shallow Aquifers ◽  
Transit Times ◽  
Tracking Model ◽  
The Mean ◽  
Transit Time Distribution ◽  
Groundwater Body

<p>In shallow aquifers, including weathered zones characteristic of crystalline geologic basements, subsurface flows strongly depend on the geomorphological evolution of landscapes as well as on the geological heterogeneity structures. Yet, it remains largely unknown how geomorphology and geology shape the residence times in the aquifers and the transit times  in the receiving stream water bodies.</p><p>We investigate this issue with 3D synthetic models of free aquifers. Aquifer models represent hillslopes from the river to the catchment divide with constant slopes, evolving widths and depths. They are submitted to uniform and constant recharge. All flows end up in the river either through the aquifer or through the surface as return flows and saturation excess overland flows. Steady-state flows and transit times to the river are simulated with Modflow and Modpath (Niswonger et al., 2011; Pollock, 2016). The mean and standard deviation of the transit time distribution are systematically determined as functions of the hillslope shapes (convergent or divergent to the river, thinning or thickening to the river) and the ratio of recharge to hydraulic conductivity.</p><p>We show that the mean transit time distribution is a function of the geology through the volume of the aquifer divided by the recharge rate even in the presence of seepage areas. The standard deviation of the transit time distribution is a function of the geomorphology through the bulk organization of the groundwater body from the river to the catchment divide. Without seepage, the organization of the groundwater body is efficiently characterized by its barycenter. When seepage occurs, the standard deviation becomes also sensitive to the extent of the seepage zone.</p><p>We conclude that mean of the transit time distribution is primarily determined by geology through the accessible aquifer volume while the ratio of the standard deviation to the mean (coefficient of variation) is rather determined by geomorphology through the profile of the aquifer from the river to the catchment divide. We discuss how geophysical data might help to determine the groundwater body and assess the transit time distribution. We illustrate these findings on natural aquifers in the crystalline basements of Brittany-Normandy (France).</p><p><strong>References</strong></p><p>Niswonger, R.G., Panday, S., Ibaraki, M., 2011. MODFLOW-NWT, A Newton formulation for MODFLOW-2005.</p><p>Pollock, D.W., 2016. User guide for MODPATH Version 7—A particle-tracking model for MODFLOW (Report No. 2016–1086), Open-File Report. Reston, VA. https://doi.org/10.3133/ofr20161086</p>

Distribution of pulmonary capillary red blood cell transit times

1995 ◽  
Vol 79 (2) ◽  
pp. 382-388 ◽  
Author(s):  
R. G. Presson ◽  
J. A. Graham ◽  
C. C. Hanger ◽  
P. S. Godbey ◽  
S. A. Gebb ◽  
...  
Keyword(s):  
Red Blood Cells ◽  
Transit Time ◽  
Blood Cells ◽  
Time Distribution ◽  
Capillary Networks ◽  
Transit Times ◽  
Pulmonary Capillary ◽  
Capillary Bed ◽  
Transit Time Distribution ◽  
Pass Through

In theory, red blood cells can pass through the pulmonary capillaries too rapidly to be completely saturated with oxygen during exercise. This idea has not been directly tested because the transit times of the fastest red blood cells are unknown. We report the first measurements of the entire transit time distribution for red blood cells crossing single subpleural capillary networks of canine lung using in vivo fluorescence videomicroscopy and compare those times with the distribution of plasma transit times in the same capillary networks. On average, plasma took 1.4 times longer than red blood cells to pass through the capillary bed. Decreased transit times with increased cardiac output were mitigated by both capillary recruitment and a narrowing of the transit time distribution. This design feature of the pulmonary capillary bed kept the shortest times from falling below the theoretical minimum time for complete oxygenation.

Hillslope permeability architecture controls on subsurface transit time distribution and flow paths

2016 ◽  
Vol 543 ◽  
pp. 17-30 ◽  
Author(s):  
A.A. Ameli ◽  
N. Amvrosiadi ◽  
T. Grabs ◽  
H. Laudon ◽  
I.F. Creed ◽  
...  
Keyword(s):  
Transit Time ◽  
Time Distribution ◽  
Flow Paths ◽  
Transit Time Distribution

scholarly journals Nonparametric lower bounds to mean transit times

2017 ◽  
Author(s):  
Earl Bardsley
Keyword(s):  
Lower Bound ◽  
Transit Time ◽  
Time Distribution ◽  
Mean Transit Time ◽  
Mean Value ◽  
System A ◽  
Lumped Parameter ◽  
Transit Times ◽  
Lumped Parameter Models ◽  
Transit Time Distribution

Abstract. Mean transit time μT, also called mean residence time, has been used widely in hydrological studies as an indicator of catchment water storage characteristics. Typically μT is estimated by the nature of catchment transformation of a natural input tracer time series. For example, increased damping and delaying of 18O seasonal isotopic variation may be taken to indicate longer mean transit times. Part of a μT estimation process involves specification of a lumped parameter flow model which provides the basis for a parametric transit time distribution. However, μT estimation has been called into question because catchment flow systems have a degree of complexity which may not justify use of simple parametric distributions. Moving toward a related index, the question is raised here as to the extent to which an arbitrary transit time distribution might enable a model mean transit time to be minimized before the fit to catchment output tracer data becomes unacceptably poor. This minimized mean value μ* represents a lower bound to μT, whatever the true transit time distribution might be. The lower bound is not necessarily an approximation to μT but might serve as an index for catchment comparisons or detect when μT is large. For a linear catchment system a simple nonparametric linear programming (LP) approach can be utilised to obtain μ*, which is conditional on a user-specified acceptable level of data fit. The LP method presented is applicable to both steady state and time-varying catchment systems and has the advantage of not requiring specification of lumped parameter models or use of explicit transit time distributions.

scholarly journals Tandem use of transit time distribution and fraction of young water reveals the dynamic flow paths supporting streamflow at a mountain headwater catchment

2021 ◽  
Author(s):  
Ravindra Dwivedi ◽  
Christopher Eastoe ◽  
John F. Knowles ◽  
Jennifer McIntosh ◽  
Thomas Meixner ◽  
...  
Keyword(s):  
Transit Time ◽  
Time Distribution ◽  
Time Series Data ◽  
Mean Transit Time ◽  
Series Data ◽  
Dynamic Flow ◽  
Deep Groundwater ◽  
Flow Paths ◽  
The Mean ◽  
Headwater Catchment

Abstract. Current understanding of the dynamic flow paths and subsurface water storages that support streamflow in mountain catchments is inhibited by the lack of long-term hydrologic data and the frequent use of single age tracers that are not applicable to older groundwater reservoirs. To address this, the current study used both multiple metrics and tracers to characterize the transient nature of flow paths with respect to change in catchment storage at Marshall Gulch, a sub-humid headwater catchment in the Santa Catalina Mountains, Arizona, USA. The fraction of streamflow that was untraceable using stable water isotope tracers was also estimated. A Gamma-type transit time distribution (TTD) was appropriate for deep groundwater analysis, but there were errors in the TTD shape parameters arising from the short record length of 3H in deep groundwater and stream water, and inconsistent seasonal cyclicity of the precipitation 3H time series data. Overall, the mean transit time calculated from 3H data was more than two decades greater than the mean transit time based on δ18O at the same site. The fraction of young water (Fyw) in shallow groundwater was estimated from δ18O time series data using weighted wavelet transform (WWT), iteratively re-weighted least squares (IRLS), and TTD-based methods. Estimates of Fyw depended on sampling frequency, the method of estimation, bedrock geology, hydroclimate, and factors affecting streamflow generation processes. The coupled use of Fyw and discharge sensitivity indicated highly dynamic flow paths that reorganized with changes in shallow catchment storage. The utility of 3H to determining Fyw in deeper groundwater was limited by data quality. Given that Fyw, discharge sensitivity, and mean transit time all yield unique information, this work demonstrates how co-application of multiple methods can yield a more complete understanding of the transient flow paths and observable storage volumes that contribute to streamflow in mountain headwater catchments.

scholarly journals The Transit-Time Distribution from the Northern Hemisphere Midlatitude Surface

2016 ◽  
Vol 73 (10) ◽  
pp. 3785-3802 ◽  
Author(s):  
Clara Orbe ◽  
Darryn W. Waugh ◽  
Paul A. Newman ◽  
Stephen Steenrod
Keyword(s):  
Northern Hemisphere ◽  
Transit Time ◽  
Time Distribution ◽  
Transport Model ◽  
Fundamental Property ◽  
Spectral Width ◽  
The Arctic ◽  
Transit Times ◽  
Fast Transport ◽  
Transit Time Distribution

Abstract The distribution of transit times from the Northern Hemisphere (NH) midlatitude surface is a fundamental property of tropospheric transport. Here, the authors present an analysis of the transit-time distribution (TTD) since air last contacted the NH midlatitude surface, as simulated by the NASA Global Modeling Initiative Chemistry Transport Model. Throughout the troposphere, the TTD is characterized by young modes and long tails. This results in mean transit times or “mean ages” Γ that are significantly larger than their corresponding modal transit times or “modal ages” τmode, especially in the NH, where Γ ≈ 0.5 yr, while τmode < 20 days. In addition, the shape of the TTD changes throughout the troposphere as the ratio of the spectral width Δ—the second temporal moment of the TTD—to the mean age decreases sharply in the NH from ~2.5 at NH high latitudes to ~0.7 in the Southern Hemisphere (SH). Decreases in Δ/Γ in the SH reflect a narrowing of the TTD relative to its mean and physically correspond to changes in the contributions of fast transport paths relative to slow eddy-diffusive recirculations. It is shown that fast transport paths control the patterns and seasonal cycles of idealized 5- and 50-day loss tracers in the Arctic and the tropics, respectively. The relationship between different TTD time scales and the idealized loss tracers, therefore, is conditional on the shape of the TTD.

scholarly journals The potential uses of tracer cycles for groundwater dating in heterogeneous aquifers

2016 ◽  
Author(s):  
Julien Farlin ◽  
Piotr Małoszewski
Keyword(s):  
Transit Time ◽  
Time Distribution ◽  
Mean Transit Time ◽  
Homogeneous Medium ◽  
Distribution Functions ◽  
Temperature Cycle ◽  
Groundwater Temperature ◽  
Groundwater Dating ◽  
The Mean ◽  
Transit Time Distribution

Abstract. The use of the annual cycles of stable isotopes to estimate the parameters of transit time distribution functions has been recently criticised by Kirchner (2016). The author shows that the mean residence time of heterogeneous catchments calculated from the damping of the amplitude of the input signal are very often over-estimates, sometimes by large factors. We show here that the overestimation depends on the relative time scales of the cycle’s frequency and the mean transit time and that tracer cycles can still be used, at least for groundwater systems sustained by baseflow. Firstly it appears that an exponential model is a good approximation for the transit time distribution of a heterogeneous groundwatershed if the subgroundwatersheds’ transit time distributions are themselves exponential and their mean transit times are in the same range or slightly higher than the period of the tracer cycle. Secondly, we suggest that tracer cycles can still be used as secondary data to test whether the degree of heterogeneity of the subsurface is small enough to warrant approximating it by a homogeneous medium. Lastly, we develop a model predicting the amplitude of groundwater temperature from the annual air temperature cycle, and show that even though temperature is not a conservative tracer, it can be useful for groundwater dating. The potential use of the temperature cycle is illustrated in the case-study of a sandstone aquifer drained by contact springs.

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