scholarly journals Identification of groundwater mean transit times of precipitation and riverbank infiltration by two‐component lumped parameter models

2019 ◽  
Vol 33 (24) ◽  
pp. 3098-3118 ◽  
Author(s):  
Nguyen Le Duy ◽  
Nguyen Viet Dung ◽  
Ingo Heidbüchel ◽  
Hanno Meyer ◽  
Markus Weiler ◽  
...  
Keyword(s):  
Lumped Parameter ◽  
Transit Times ◽  
Lumped Parameter Models ◽  
Two Component

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 Aggregation effects on tritium-based mean transit times and young water fractions in spatially heterogeneous catchments and groundwater systems

2017 ◽  
Vol 21 (9) ◽  
pp. 4615-4627 ◽  
Author(s):  
Michael K. Stewart ◽  
Uwe Morgenstern ◽  
Maksym A. Gusyev ◽  
Piotr Małoszewski
Keyword(s):  
Spatial Heterogeneity ◽  
Aggregation Bias ◽  
Virtual Experiments ◽  
Lumped Parameter ◽  
Transit Times ◽  
Lumped Parameter Models ◽  
Groundwater Systems ◽  
Water Fractions ◽  
The Mean ◽  
Groundwater Wells

Abstract. Kirchner (2016a) demonstrated that aggregation errors due to spatial heterogeneity, represented by two homogeneous subcatchments, could cause severe underestimation of the mean transit times (MTTs) of water travelling through catchments when simple lumped parameter models were applied to interpret seasonal tracer cycle data. Here we examine the effects of such errors on the MTTs and young water fractions estimated using tritium concentrations in two-part hydrological systems. We find that MTTs derived from tritium concentrations in streamflow are just as susceptible to aggregation bias as those from seasonal tracer cycles. Likewise, groundwater wells or springs fed by two or more water sources with different MTTs will also have aggregation bias. However, the transit times over which the biases are manifested are different because the two methods are applicable over different time ranges, up to 5 years for seasonal tracer cycles and up to 200 years for tritium concentrations. Our virtual experiments with two water components show that the aggregation errors are larger when the MTT differences between the components are larger and the amounts of the components are each close to 50 % of the mixture. We also find that young water fractions derived from tritium (based on a young water threshold of 18 years) are almost immune to aggregation errors as were those derived from seasonal tracer cycles with a threshold of about 2 months.

scholarly journals Aggregation effects on tritium-based mean transit times and young water fractions in spatially heterogeneous catchments and groundwater systems, and implications for past and future applications of tritium

2016 ◽  
Author(s):  
Michael K. Stewart ◽  
Uwe Morgenstern ◽  
Maksym A. Gusyev ◽  
Piotr Maloszewski
Keyword(s):  
Heterogeneous Systems ◽  
Lumped Parameter Model ◽  
Aggregation Bias ◽  
System Parameters ◽  
Lumped Parameter ◽  
Transit Times ◽  
Lumped Parameter Models ◽  
Groundwater Systems ◽  
Water Fractions ◽  
The Mean

Abstract. Applications of simple lumped parameter models to describe aspects of hydrological systems rest on assumptions of homogeneity that are rarely valid. The lumped parameters are supposed to represent the quantities within the system as well as those of the overall system, but such quantities will obviously vary greatly from place to place within heterogeneous systems. Less appreciated is the fact that aggregation errors will affect overall system parameters as well. Kirchner (2016a) recently demonstrated that aggregation errors due to heterogeneity in catchments could cause severe underestimation of the mean transit times (MTTs) of water travelling through catchments when simple lumped parameter models were applied to interpret seasonal tracer cycles. Here we examine the effects of such errors on the MTTs and young water fractions estimated using tritium concentrations. We find that MTTs derived from tritium concentrations in streamflow are just as susceptible to aggregation bias as those from seasonal tracer cycles. Likewise, groundwater wells or springs fed by two or more water sources with different MTTs will also show aggregation bias. However, the transit times over which the biases are manifested are very different; for seasonal tracer cycles it is 2–3 months up to about 5 years, while for tritium concentrations it is 6–12 years up to about 200 years. We also find that young water fractions derived from tritium are almost immune to aggregation errors as were those derived from seasonal tracer cycles. To investigate the implications of these findings for past and future use of tritium for estimating MTTs in catchments and groundwater systems, we examined case studies from the literature in which simple and more complicated lumped parameter models had been used. We find that MTT aggregation errors are small when either component waters are young (less than 6–12 years, as found in many catchments), or component waters have similar MTTs to each other. On the other hand, aggregation errors are large when very young water components are mixed with old components. In general, well-chosen compound lumped parameter models should be used as they will eliminate potential aggregation errors due to the application of simple lumped parameter models. The choice of a suitable lumped parameter model can be assisted by matching simulations to time series of tritium measurements (underlining the value of long series of tritium measurements), but such results should also be finally validated to ensure that the parameters found by modelling correspond to reality.

scholarly journals Understanding mean transit times in Andean tropical montane cloud forest catchments: combining tracer data, lumped parameter models and uncertainty analysis

2013 ◽  
Vol 10 (12) ◽  
pp. 15871-15914 ◽  
Author(s):  
E. Timbe ◽  
D. Windhorst ◽  
P. Crespo ◽  
H.-G. Frede ◽  
J. Feyen ◽  
...  
Keyword(s):  
Surface Waters ◽  
Goodness Of Fit ◽  
Stream Water ◽  
Cloud Forest ◽  
Soil Layer ◽  
Distribution Functions ◽  
Lumped Parameter ◽  
Transit Times ◽  
Lumped Parameter Models ◽  
Piston Flow

Abstract. Weekly samples from surface waters, springs, soil water and rainfall were collected in a 76.9 km2 mountain rain forest catchment and its tributaries in southern Ecuador. Time series of the stable water isotopes δ18O and δ2H were used to calculate mean transit times (MTTs) and the transit time distribution functions (TTDs) solving the convolution method for seven lumped parameter models. For each model setup, the Generalized Likelihood Uncertainty Estimation (GLUE) methodology was applied to find the best predictions, behavioral solutions and parameter identifiability. For the study basin, TTDs based on model types such as the Linear-Piston Flow for soil waters and the Exponential-Piston Flow for surface waters and springs performed better than more versatile equations such as the Gamma and the Two Parallel Linear Reservoirs. Notwithstanding both approaches yielded a better goodness of fit for most sites, but with considerable larger uncertainty shown by GLUE. Among the tested models, corresponding results were obtained for soil waters with short MTTs (ranging from 3 to 12 weeks). For waters with longer MTTs differences were found, suggesting that for those cases the MTT should be based at least on an intercomparison of several models. Under dominant baseflow conditions long MTTs for stream water ≥2 yr were detected, a phenomenon also observed for shallow springs. Short MTTs for water in the top soil layer indicate a rapid exchange of surface waters with deeper soil horizons. Differences in travel times between soils suggest that there is evidence of a land use effect on flow generation.

scholarly journals Mean Transit Times in Headwater Catchments: Insights from the Otway Ranges, Australia

2017 ◽  
Author(s):  
William Howcroft ◽  
Ian Cartwright ◽  
Uwe Morgenstern
Keyword(s):  
Stream Water ◽  
Anthropogenic Activities ◽  
Discharge Data ◽  
Headwater Catchments ◽  
Stream Discharge ◽  
Lumped Parameter ◽  
Transit Times ◽  
Lumped Parameter Models ◽  
Bush Fire ◽  
Major Ion Geochemistry

Abstract. Understanding the timescales of water flow through catchments and the origins of stream water at different flow conditions is critical for understanding catchment behaviour and managing water resources. Here, tritium (3H) activities, major ion geochemistry and discharge data were used in conjunction with Lumped Parameter Models (LPMs) to investigate mean transit times (MTTs) and the stores of water in six headwater catchments of the Otway Ranges in southeast Australia. 3H activities of stream water ranged from 0.20 to 2.14 TU, which are far lower than those of modern local rainfall (2.4 to 3.2 TU). The 3H activities of the stream water are lowest during the low summer flows and increase with stream discharge. Calculated MTTs vary from approximately 7 to 234 years which, in many cases, exceed those reported for river systems globally. The MTT estimates, however, are subject to a number of uncertainties, including, uncertainties in the most appropriate LPM to use, aggregation errors, and uncertainty in the modern and bomb-pulse 3H activity of rainfall. These uncertainties locally result in uncertainties in MTTs of several years; however, they do not change the overall conclusions that the water in these streams has MTTs of several years to decades. There is discharge threshold of approximately 104 m3 day−1 in all catchments above which 3H activities do not increase appreciably above ~ 2.0 TU. The MTT of this 3H activity is approximately ten years, which implies that changes within the catchments, including drought, deforestation, land use and/or bush fire, would not be realised within the streams for at least a decade. A positive correlation exists between 3H activities and nitrate and sulphate concentrations within several of the catchments, which suggests that anthropogenic activities have increasingly impacted water quality at these locations over time.

scholarly journals Understanding uncertainties when inferring mean transit times of water trough tracer-based lumped-parameter models in Andean tropical montane cloud forest catchments

2014 ◽  
Vol 18 (4) ◽  
pp. 1503-1523 ◽  
Author(s):  
E. Timbe ◽  
D. Windhorst ◽  
P. Crespo ◽  
H.-G. Frede ◽  
J. Feyen ◽  
...  
Keyword(s):  
Surface Waters ◽  
Goodness Of Fit ◽  
Stream Water ◽  
Cloud Forest ◽  
Soil Layer ◽  
Distribution Functions ◽  
Lumped Parameter ◽  
Transit Times ◽  
Lumped Parameter Models ◽  
Piston Flow

Abstract. Weekly samples from surface waters, springs, soil water and rainfall were collected in a 76.9 km2 mountain rain forest catchment and its tributaries in southern Ecuador. Time series of the stable water isotopes δ18O and δ2H were used to calculate mean transit times (MTTs) and the transit time distribution functions (TTDs) solving the convolution method for seven lumped-parameter models. For each model setup, the generalized likelihood uncertainty estimation (GLUE) methodology was applied to find the best predictions, behavioral solutions and parameter identifiability. For the study basin, TTDs based on model types such as the linear–piston flow for soil waters and the exponential–piston flow for surface waters and springs performed better than more versatile equations such as the gamma and the two parallel linear reservoirs. Notwithstanding both approaches yielded a better goodness of fit for most sites, but with considerable larger uncertainty shown by GLUE. Among the tested models, corresponding results were obtained for soil waters with short MTTs (ranging from 2 to 9 weeks). For waters with longer MTTs differences were found, suggesting that for those cases the MTT should be based at least on an intercomparison of several models. Under dominant baseflow conditions long MTTs for stream water ≥ 2 yr were detected, a phenomenon also observed for shallow springs. Short MTTs for water in the top soil layer indicate a rapid exchange of surface waters with deeper soil horizons. Differences in travel times between soils suggest that there is evidence of a land use effect on flow generation.

Lumped parameter models for two-ventricle and healthy and failing extracardiac Fontan circulations

2021 ◽  
Author(s):  
Matthew G Doyle ◽  
Marina Chugunova ◽  
S Lucy Roche ◽  
James P Keener
Keyword(s):  
Single Ventricle ◽  
Left Ventricular ◽  
Sensitivity Analyses ◽  
Surgical Strategies ◽  
Lumped Parameter ◽  
Lumped Parameter Models ◽  
Fontan Failure ◽  
Existence Of Periodic Solutions ◽  
Mathematical Definitions ◽  
Extracardiac Fontan

Abstract Fontan circulations are surgical strategies to treat infants born with single ventricle physiology. Clinical and mathematical definitions of Fontan failure are lacking, and understanding is needed of parameters indicative of declining physiologies. Our objective is to develop lumped parameter models of two-ventricle and single-ventricle circulations. These models, their mathematical formulations and a proof of existence of periodic solutions are presented. Sensitivity analyses are performed to identify key parameters. Systemic venous and systolic left ventricular compliances and systemic capillary and pulmonary venous resistances are identified as key parameters. Our models serve as a framework to study the differences between two-ventricle and single-ventricle physiologies and healthy and failing Fontan circulations.

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