scholarly journals Aggregation in environmental systems – Part 1: Seasonal tracer cycles quantify young water fractions, but not mean transit times, in spatially heterogeneous catchments

2016 ◽  
Vol 20 (1) ◽  
pp. 279-297 ◽  
Author(s):  
J. W. Kirchner
Keyword(s):  
Transit Time ◽  
Mean Transit Time ◽  
Strong Nonlinearity ◽  
Isotopic Tracers ◽  
Water Fraction ◽  
Benchmark Tests ◽  
Environmental Systems ◽  
Transit Times ◽  
Event Based ◽  
The Relationship

Abstract. Environmental heterogeneity is ubiquitous, but environmental systems are often analyzed as if they were homogeneous instead, resulting in aggregation errors that are rarely explored and almost never quantified. Here I use simple benchmark tests to explore this general problem in one specific context: the use of seasonal cycles in chemical or isotopic tracers (such as Cl−, δ18O, or δ2H) to estimate timescales of storage in catchments. Timescales of catchment storage are typically quantified by the mean transit time, meaning the average time that elapses between parcels of water entering as precipitation and leaving again as streamflow. Longer mean transit times imply greater damping of seasonal tracer cycles. Thus, the amplitudes of tracer cycles in precipitation and streamflow are commonly used to calculate catchment mean transit times. Here I show that these calculations will typically be wrong by several hundred percent, when applied to catchments with realistic degrees of spatial heterogeneity. This aggregation bias arises from the strong nonlinearity in the relationship between tracer cycle amplitude and mean travel time. I propose an alternative storage metric, the young water fraction in streamflow, defined as the fraction of runoff with transit times of less than roughly 0.2 years. I show that this young water fraction (not to be confused with event-based "new water" in hydrograph separations) is accurately predicted by seasonal tracer cycles within a precision of a few percent, across the entire range of mean transit times from almost zero to almost infinity. Importantly, this relationship is also virtually free from aggregation error. That is, seasonal tracer cycles also accurately predict the young water fraction in runoff from highly heterogeneous mixtures of subcatchments with strongly contrasting transit-time distributions. Thus, although tracer cycle amplitudes yield biased and unreliable estimates of catchment mean travel times in heterogeneous catchments, they can be used to reliably estimate the fraction of young water in runoff.

scholarly journals Aggregation in environmental systems: seasonal tracer cycles quantify young water fractions, but not mean transit times, in spatially heterogeneous catchments

2015 ◽  
Vol 12 (3) ◽  
pp. 3059-3103 ◽  
Author(s):  
J. W. Kirchner
Keyword(s):  
Transit Time ◽  
Mean Transit Time ◽  
Strong Nonlinearity ◽  
Isotopic Tracers ◽  
Water Fraction ◽  
Benchmark Tests ◽  
Environmental Systems ◽  
Transit Times ◽  
Event Based ◽  
The Relationship

Abstract. Environmental heterogeneity is ubiquitous, but environmental systems are often analyzed as if they were homogeneous instead, resulting in aggregation errors that are rarely explored and almost never quantified. Here I use simple benchmark tests to explore this general problem in one specific context: the use of seasonal cycles in chemical or isotopic tracers (such as Cl−, δ18O, or δ2H) to estimate timescales of storage in catchments. Timescales of catchment storage are typically quantified by the mean transit time, meaning the average time that elapses between parcels of water entering as precipitation and leaving again as streamflow. Longer mean transit times imply greater damping of seasonal tracer cycles. Thus, the amplitudes of tracer cycles in precipitation and streamflow are commonly used to calculate catchment mean transit times. Here I show that these calculations will typically be wrong by several hundred percent, when applied to catchments with realistic degrees of spatial heterogeneity. This aggregation bias arises from the strong nonlinearity in the relationship between tracer cycle amplitude and mean travel time. I propose an alternative storage metric, the young water fraction in streamflow, defined as the fraction of runoff with transit times of less than roughly 0.2 years. I show that this young water fraction (not to be confused with event-based "new water" in hydrograph separations) is accurately predicted by seasonal tracer cycles within a precision of a few percent, across the entire range of mean transit times from almost zero to almost infinity. Importantly, this relationship is also virtually free from aggregation error. That is, seasonal tracer cycles also accurately predict the young water fraction in runoff from highly heterogeneous mixtures of subcatchments with strongly contrasting transit time distributions. Thus, although tracer cycle amplitudes yield biased and unreliable estimates of catchment mean travel times in heterogeneous catchments, they can be used reliably to estimate the fraction of young water in runoff.

scholarly journals Assessment of hydrological pathways in East African montane catchments under different land use

2018 ◽  
Vol 22 (9) ◽  
pp. 4981-5000 ◽  
Author(s):  
Suzanne R. Jacobs ◽  
Edison Timbe ◽  
Björn Weeser ◽  
Mariana C. Rufino ◽  
Klaus Butterbach-Bahl ◽  
...  
Keyword(s):  
Land Use ◽  
Transit Time ◽  
Stream Water ◽  
Mean Transit Time ◽  
Natural Forest ◽  
Smallholder Agriculture ◽  
Tea Plantation ◽  
Water Fraction ◽  
Transit Times ◽  
Water Isotope

Abstract. Conversion of natural forest (NF) to other land uses could lead to significant changes in catchment hydrology, but the nature of these changes has been insufficiently investigated in tropical montane catchments, especially in Africa. To address this knowledge gap, we aimed to identify stream water (RV) sources and flow paths in three tropical montane sub-catchments (27–36 km2) with different land use (natural forest, NF; smallholder agriculture, SHA; and commercial tea and tree plantations, TTP) within a 1021 km2 catchment in the Mau Forest complex, Kenya. Weekly samples were collected from stream water, precipitation (PC) and mobile soil water for 75 weeks and analysed for stable isotopes of water (δ2H and δ18O) for mean transit time (MTT) estimation with two lumped parameter models (gamma model, GM; and exponential piston flow model, EPM) and for the calculation of the young water fraction. Weekly samples from stream water and potential endmembers were collected over a period of 55 weeks and analysed for Li, Na, Mg, K, Rb, Sr and Ba for endmember mixing analysis (EMMA). Solute concentrations in precipitation were lower than in stream water in all catchments (p < 0.05), whereas concentrations in springs, shallow wells and wetlands were generally more similar to stream water. The stream water isotope signal was considerably damped compared to the isotope signal in precipitation. Mean transit time analysis suggested long transit times for stream water (up to 4 years) in the three sub-catchments, but model efficiencies were very low. The young water fraction ranged from 13 % in the smallholder agriculture sub-catchment to 15 % in the tea plantation sub-catchment. Mean transit times of mobile soil water ranged from 3.2–3.3 weeks in forest soils and 4.5–7.9 weeks in pasture soils at 15 cm depth to 10.4–10.8 weeks in pasture soils at 50 cm depth. The contribution of springs and wetlands to stream discharge increased from a median of 16.5 (95 % confidence interval: 11.3–22.9), 2.1 (−3.0–24.2) and 50.2 (30.5–65.5) % during low flow to 20.7 (15.2–34.7), 53.0 (23.0–91.3) and 69.4 (43.0–123.9) % during high flow in the natural forest, smallholder agriculture and tea plantation sub-catchments, respectively. Our results indicate that groundwater is an important component of stream water, irrespective of land use. The results further suggest that the selected transit time models and tracers might not be appropriate in tropical catchments with highly damped stream water isotope signatures. A more in-depth investigation of the discharge dependence of the young water fraction and transit time estimation using other tracers, such as tritium, could therefore shed more light on potential land use effects on the hydrological behaviour of tropical montane catchments.

scholarly journals Quantifying new water fractions and transit time distributions using ensemble hydrograph separation: theory and benchmark tests

2019 ◽  
Vol 23 (1) ◽  
pp. 303-349 ◽  
Author(s):  
James W. Kirchner
Keyword(s):  
Transit Time ◽  
Time Lag ◽  
Isotopic Fractionation ◽  
Hydrograph Separation ◽  
Isotopic Tracers ◽  
Water Fraction ◽  
Benchmark Tests ◽  
Water Fractions ◽  
Lag Times ◽  
Over Time

Abstract. Decades of hydrograph separation studies have estimated the proportions of recent precipitation in streamflow using end-member mixing of chemical or isotopic tracers. Here I propose an ensemble approach to hydrograph separation that uses regressions between tracer fluctuations in precipitation and discharge to estimate the average fraction of new water (e.g., same-day or same-week precipitation) in streamflow across an ensemble of time steps. The points comprising this ensemble can be selected to isolate conditions of particular interest, making it possible to study how the new water fraction varies as a function of catchment and storm characteristics. Even when new water fractions are highly variable over time, one can show mathematically (and confirm with benchmark tests) that ensemble hydrograph separation will accurately estimate their average. Because ensemble hydrograph separation is based on correlations between tracer fluctuations rather than on tracer mass balances, it does not require that the end-member signatures are constant over time, or that all the end-members are sampled or even known, and it is relatively unaffected by evaporative isotopic fractionation. Ensemble hydrograph separation can also be extended to a multiple regression that estimates the average (or “marginal”) transit time distribution (TTD) directly from observational data. This approach can estimate both “backward” transit time distributions (the fraction of streamflow that originated as rainfall at different lag times) and “forward” transit time distributions (the fraction of rainfall that will become future streamflow at different lag times), with and without volume-weighting, up to a user-determined maximum time lag. The approach makes no assumption about the shapes of the transit time distributions, nor does it assume that they are time-invariant, and it does not require continuous time series of tracer measurements. Benchmark tests with a nonlinear, nonstationary catchment model confirm that ensemble hydrograph separation reliably quantifies both new water fractions and transit time distributions across widely varying catchment behaviors, using either daily or weekly tracer concentrations as input. Numerical experiments with the benchmark model also illustrate how ensemble hydrograph separation can be used to quantify the effects of rainfall intensity, flow regime, and antecedent wetness on new water fractions and transit time distributions.

scholarly journals Quantifying new water fractions and transit time distributions using ensemble hydrograph separation: theory and benchmark tests

2018 ◽  
Author(s):  
James Kirchner
Keyword(s):  
Transit Time ◽  
Isotopic Fractionation ◽  
Hydrograph Separation ◽  
Isotopic Tracers ◽  
Water Fraction ◽  
Benchmark Tests ◽  
Water Fractions ◽  
Lag Times ◽  
Storm Characteristics ◽  
Over Time

Abstract. Decades of hydrograph separation studies have estimated the proportions of recent precipitation in streamflow using end-member mixing of chemical or isotopic tracers. Here I propose an ensemble approach to hydrograph separation that uses regressions between tracer fluctuations in precipitation and discharge to estimate the average fraction of new water (e.g., same-day or same-week precipitation) in streamflow across an ensemble of time steps. The points comprising this ensemble can be selected to isolate conditions of particular interest, making it possible to study how the new water fraction varies as a function of catchment and storm characteristics. Even when new water fractions are highly variable over time, one can show mathematically (and confirm with benchmark tests) that ensemble hydrograph separation will accurately estimate their average. Because ensemble hydrograph separation is based on correlations between tracer fluctuations rather than on tracer mass balances, it does not require that the end-member signatures are constant over time, or that all the end-members are sampled or even known, and it is relatively unaffected by evaporative isotopic fractionation. Ensemble hydrograph separation can also be extended to a multiple regression that estimates the average (or "marginal") transit time distribution directly from observational data. This approach can estimate both "backward" transit time distributions (the fraction of streamflow that originated as rainfall at different lag times) and "forward" transit time distributions (the fraction of rainfall that will become future streamflow at different lag times), with and without volume-weighting. It makes no assumption about the shapes of the transit time distributions, nor does it assume that they are time-invariant, and it does not require continuous time series of tracer measurements. Benchmark tests with a nonlinear, nonstationary catchment model confirm that ensemble hydrograph separation reliably quantifies both new water fractions and transit time distributions across widely varying catchment behaviors, using either daily or weekly tracer concentrations as input. Numerical experiments with the benchmark model also illustrate how ensemble hydrograph separation can be used to quantify the effects of rainfall intensity, flow regime, and antecedent wetness on new water fractions and transit time distributions.

Regional differences in erythrocyte transit in normal lungs

1985 ◽  
Vol 59 (4) ◽  
pp. 1266-1271 ◽  
Author(s):  
J. C. Hogg ◽  
B. A. Martin ◽  
S. Lee ◽  
T. McLean
Keyword(s):  
Blood Volume ◽  
Transit Time ◽  
Regional Differences ◽  
Regional Blood Flow ◽  
Mean Transit Time ◽  
Vascular Bed ◽  
Transit Times ◽  
Regional Blood Volume ◽  
The Relationship ◽  
Normal Lungs

We measured regional blood volume and flow in the lungs of nine mongrel dogs. The time taken for the erythrocytes to transit through individual lung regions was calculated from the relationship t = V/Q, where V is blood volume and Q is flow. The data show that the total pulmonary blood volume was 82 +/- 6 ml and that the average time spent in the pulmonary vascular bed was 2.86 +/- 0.31 s. The frequency distribution of the transit times ranged from 0.41 to 6 s in the experiment with the shortest mean transit (1.62 s) and from 0.9 to greater than 20 s in the experiment with the longest mean transit time (4.6 s). The regional data show that the longer transit times were in the upper lung and that expansion of the blood volume as flow increased down the lung prevented an excessive shortening of the transit time. We conclude that increasing regional blood flow is associated with an expansion of regional blood volumes so that the transit times remain relatively constant.

Transit time dispersion in the pulmonary arterial tree

1998 ◽  
Vol 85 (2) ◽  
pp. 565-574 ◽  
Author(s):  
Anne V. Clough ◽  
Steven T. Haworth ◽  
Christopher C. Hanger ◽  
Jerri Wang ◽  
David L. Roerig ◽  
...  
Keyword(s):  
Transit Time ◽  
Mean Transit Time ◽  
Arterial Tree ◽  
Lung Lobe ◽  
Transit Times ◽  
Pulmonary Capillary ◽  
Time Dispersion ◽  
Pulmonary Arterial ◽  
The Difference ◽  
In Transit

Knowledge of the contributions of arterial and venous transit time dispersion to the pulmonary vascular transit time distribution is important for understanding lung function and for interpreting various kinds of data containing information about pulmonary function. Thus, to determine the dispersion of blood transit times occurring within the pulmonary arterial and venous trees, images of a bolus of contrast medium passing through the vasculature of pump-perfused dog lung lobes were acquired by using an X-ray microfocal angiography system. Time-absorbance curves from the lobar artery and vein and from selected locations within the intrapulmonary arterial tree were measured from the images. Overall dispersion within the lung lobe was determined from the difference in the first and second moments (mean transit time and variance, respectively) of the inlet arterial and outlet venous time-absorbance curves. Moments at selected locations within the arterial tree were also calculated and compared with those of the lobar artery curve. Transit times for the arterial pathways upstream from the smallest measured arteries (200-μm diameter) were less than ∼20% of the total lung lobe mean transit time. Transit time variance among these arterial pathways (interpathway dispersion) was less than ∼5% of the total variance imparted on the bolus as it passed through the lung lobe. On average, the dispersion that occurred along a given pathway (intrapathway dispersion) was negligible. Similar results were obtained for the venous tree. Taken together, the results suggest that most of the variation in transit time in the intrapulmonary vasculature occurs within the pulmonary capillary bed rather than in conducting arteries or veins.

scholarly journals Aggregation in environmental systems: catchment mean transit times and young water fractions under hydrologic nonstationarity

2015 ◽  
Vol 12 (3) ◽  
pp. 3105-3167 ◽  
Author(s):  
J. W. Kirchner
Keyword(s):  
Direct Determination ◽  
Weighted Average ◽  
Flow Regimes ◽  
Box Model ◽  
Water Age ◽  
Isotopic Tracers ◽  
Water Fraction ◽  
Transit Times ◽  
Precipitation Seasonality ◽  
Water Fractions

Abstract. Methods for estimating mean transit times from chemical or isotopic tracers (such as Cl−, δ18O, or δ2H) commonly assume that catchments are stationary (i.e. time-invariant) and homogeneous. Real catchments are neither. In a companion paper, I showed that catchment mean transit times estimated from seasonal tracer cycles are highly vulnerable to aggregation error, exhibiting strong bias and large scatter in spatially heterogeneous catchments. I proposed a different measure of transit times, the young water fraction, and showed that it is virtually immune to aggregation error under spatial heterogeneity. Here I extend this analysis by exploring how nonstationarity affects mean transit times and young water fractions estimated from seasonal tracer cycles, using benchmark tests based on a simple two-box model. The model exhibits complex nonstationary behavior, with striking volatility in tracer concentrations, young water fractions, and mean transit times, driven by rapid shifts in the mixing ratios of fluxes from the upper and lower boxes. The transit-time distribution in streamflow becomes increasingly skewed at higher discharges, with marked increases in the young water fraction and decreases in the mean water age, reflecting the increased dominance of the upper box at higher flows. Even this simple two-box model exhibits strong equifinality; hydrograph calibration cannot constrain four of its five parameters. This equifinality problem can be partly resolved by simple parameter transformations. However, transit times are primarily determined by residual storage, which cannot be constrained through hydrograph calibration and must instead be estimated by tracer behavior. Seasonal tracer cycles in the two-box model are very poor predictors of mean transit times, with typical errors of several hundred percent. However, the same tracer cycles predict young water fractions within a few percent, even in model catchments that are both nonstationary and spatially heterogeneous (although they may be biased by roughly 0.1–0.2 at sites where strong precipitation seasonality is correlated with precipitation tracer concentrations). Flow-weighted fits to the seasonal tracer cycles accurately predict the flow-weighted average young water fraction in streamflow, while unweighted fits to the seasonal tracer cycles accurately predict the unweighted average young water fraction. Young water fractions can also be estimated separately for individual flow regimes, again with a precision of a few percent, allowing direct determination of how shifts in hydraulic regime alter the fraction of water reaching the stream by fast flowpaths. One can also estimate the chemical composition of idealized "young water" and "old water" end-members, using relationships between young water fractions and solute concentrations across different flow regimes. These results demonstrate that mean transit times cannot be estimated reliably from seasonal tracer cycles, and that, by contrast, the young water fraction is a robust and useful metric of transit times, even in catchments that exhibit strong nonstationarity and heterogeneity.

A Simple and Rapid Non-Invasive Radioisotope Method to Determine Ventricular Ejection Fractions and Cardiopulmonary Transit Times

1977 ◽  
Vol 16 (02) ◽  
pp. 57-62
Author(s):  
A. Ahonen ◽  
J. Kuikka
Keyword(s):  
Ejection Fraction ◽  
Right Ventricle ◽  
Transit Time ◽  
Mean Transit Time ◽  
Left Ventricular ◽  
Ventricular Ejection ◽  
Ventricular Ejection Fraction ◽  
Non Invasive ◽  
Transit Times ◽  
Whole Heart

SummaryEjection fractions and cardiopulmonary transit times were measured in 20 hospital patients by means of intravenously injected 99mTc-radiocardiography. Time activity curves from the regions of the whole heart, superior vena cava, right atrium, right ventricle, right lung, left atrium and left ventricle were drawn and analyzed by using the modified gamma function fitting method. The comparison between the ejection fractions determined from the whole heart curves and those from the ventricular curves shows a correlation coefficient of 0.93 for the right ventricle and of 0.90 for the left, although there was a systematic difference between the determinations. The analysis of the single ventricular curves gave about 10 per cent higher values than those obtained from the whole heart curvesThe cardiopulmonary parameters measured from the whole heart curves for 16 normal subjects the following results gave:right ventricular ejection fraction = 0.57 ± 0.08left ventricular ejection fraction = 0.62 ± 0.08pulmonary mean transit time = 6.1 ± 1.1 heart-beatsintracardiac mean transit time = 10.5 ± 1.8 heartbeatsright/left ventricular volume = 1.10 ± 0.09These values agree closely with the data accumulated using more elaborate methods. The method presented here is simple to perform, it is non-invasive, time-saving, inexpensive, easy to analyze and suitable for exercising subjects and for bed-side measurements. Data assembly and analysis are easily automated so that results are obtainable immediately after measurements.

scholarly journals Transit times from rainfall to baseflow in headwater catchments estimated using tritium: the Ovens River, Australia

2015 ◽  
Vol 19 (9) ◽  
pp. 3771-3785 ◽  
Author(s):  
I. Cartwright ◽  
U. Morgenstern
Keyword(s):  
Transit Time ◽  
Headwater Streams ◽  
Stream Water ◽  
Mean Transit Time ◽  
Significant Proportion ◽  
Low Flow ◽  
Flow Conditions ◽  
Headwater Catchments ◽  
Flow Models ◽  
Transit Times

Abstract. Headwater streams contribute a significant proportion of the total flow to many river systems, especially during summer low-flow periods. However, despite their importance, the time taken for water to travel through headwater catchments and into the streams (the transit time) is poorly understood. Here, 3H activities of stream water are used to define transit times of water contributing to streams from the upper reaches of the Ovens River in south-east Australia at varying flow conditions. 3H activities of the stream water varied from 1.63 to 2.45 TU, which are below the average 3H activity of modern local rainfall (2.85 to 2.99 TU). The highest 3H activities were recorded following higher winter flows and the lowest 3H activities were recorded at summer low-flow conditions. Variations of major ion concentrations and 3H activities with streamflow imply that different stores of water from within the catchment (e.g. from the soil or regolith) are mobilised during rainfall events rather than there being simple dilution of an older groundwater component by event water. Mean transit times calculated using an exponential-piston flow model range from 4 to 30 years and are higher at summer low-flow conditions. Mean transit times calculated using other flow models (e.g. exponential flow or dispersion) are similar. There are broad correlations between 3H activities and the percentage of rainfall exported from each catchment and between 3H activities and Na and Cl concentrations that allow first-order estimates of mean transit times in adjacent catchments or at different times in these catchments to be made. Water from the upper Ovens River has similar mean transit times to the headwater streams implying there is no significant input of old water from the alluvial gravels. The observation that the water contributing to the headwater streams in the Ovens catchment has a mean transit time of years to decades implies that these streams are buffered against rainfall variations on timescales of a few years. However, impacts of any changes to land use in these catchments may take years to decades to manifest themselves in changes to streamflow or water quality.

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