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.

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 Sampling frequency trade-offs in the assessment of mean transit times of tropical montane catchment waters under semi-steady-state conditions

2015 ◽  
Vol 19 (3) ◽  
pp. 1153-1168 ◽  
Author(s):  
E. Timbe ◽  
D. Windhorst ◽  
R. Celleri ◽  
L. Timbe ◽  
P. Crespo ◽  
...  
Keyword(s):  
Cloud Forest ◽  
Sampling Frequency ◽  
Distribution Functions ◽  
Precipitation Event ◽  
Parameter Distribution ◽  
Water Type ◽  
Clear Trend ◽  
Trade Offs ◽  
Transit Times ◽  
Piston Flow

Abstract. Precipitation event samples and weekly based water samples from streams and soils were collected in a tropical montane cloud forest catchment for 2 years and analyzed for stable water isotopes in order to understand the effect of sampling frequency in the performance of three lumped-parameter distribution functions (exponential-piston flow, linear-piston flow and gamma) which were used to estimate mean transit times of waters. Precipitation data, used as input function for the models, were aggregated to daily, weekly, bi-weekly, monthly and bi-monthly sampling resolutions, while analyzed frequencies for outflows went from weekly to bi-monthly. By using different scenarios involving diverse sampling frequencies, this study reveals that the effect of lowering the sampling frequency depends on the water type. For soil waters, with transit times on the order of few weeks, there was a clear trend of over predictions. In contrast, the trend for stream waters, which have a more damped isotopic signal and mean transit times on the order of 2 to 4 years, was less clear and showed a dependence on the type of model used. The trade-off to coarse data resolutions could potentially lead to misleading conclusions on how water actually moves through the catchment, notwithstanding that these predictions could reach better fitting efficiencies, fewer uncertainties, errors and biases. For both water types an optimal sampling frequency seems to be 1 or at most 2 weeks. The results of our analyses provide information for the planning of future fieldwork in similar Andean or other catchments.

scholarly journals Sampling frequency trade-offs in the assessment of mean transit times of tropical montane catchment waters under semi-steady-state conditions

2014 ◽  
Vol 11 (11) ◽  
pp. 12443-12488
Author(s):  
E. Timbe ◽  
D. Windhorst ◽  
R. Celleri ◽  
L. Timbe ◽  
P. Crespo ◽  
...  
Keyword(s):  
Cloud Forest ◽  
Sampling Frequency ◽  
Distribution Functions ◽  
Precipitation Event ◽  
Water Type ◽  
Clear Trend ◽  
Temporal Sampling ◽  
Trade Offs ◽  
Transit Times ◽  
Piston Flow

Abstract. Stream and soil waters were collected on a weekly basis in a tropical montane cloud forest catchment for two years and analyzed for stable water isotopes in order to infer transit time distribution functions and to define the mean transit times. Depending on the water type (stream or soil water), lumped distribution functions such as Exponential-Piston flow, Linear-Piston flow and Gamma models using temporal isotopic variations of precipitation event samples as input, were fitted. Samples were aggregated to daily, weekly, biweekly, monthly and bimonthly time scales in order to check the sensitivity of temporal sampling on model predictions. The study reveals that the effect of decreasing sampling frequency depends on the water type. For soil waters with transit times in the order of weeks to months, there was a clear trend of over prediction. In contrast, the trend of prediction for stream waters, with a dampened isotopic signal and mean transit times in the order of 2 to 4 years, was less clear and depending on the type of model used. The trade-off to coarse data resolutions could potentially lead to misleading conclusions on how water actually moves through the catchment, while at the same time predictions can reach better fitting efficiencies, lesser uncertainties, errors and biases. For both water types an optimal sampling frequency seems to be one or at most two weeks. The results of our analyses provide information for the planning (in particular in terms of cost-benefit and time requirements) of future fieldwork in similar Andean or other catchments.

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.

Characterization of pulmonary arterial input impedance with lumped parameter models

1987 ◽  
Vol 252 (3) ◽  
pp. H585-H593 ◽  
Author(s):  
B. J. Grant ◽  
L. J. Paradowski
Keyword(s):  
Input Impedance ◽  
Goodness Of Fit ◽  
Arterial Compliance ◽  
Characteristic Impedance ◽  
Lumped Parameter Model ◽  
Pulmonary Vasculature ◽  
Impedance Spectra ◽  
Lumped Parameter ◽  
Lumped Parameter Models ◽  
Pulmonary Arterial

The purpose of this study is to evaluate systematically the ability of lumped parameter models to approximate pulmonary arterial input impedance (Zin) and estimate characteristic impedance (Zc) and pulmonary arterial compliance (Cart). To assess goodness of fit, the parameters of each model were adjusted so that the model's impedance approximates the Zin measured in anesthetized cats. To assess the ability of the model to estimate Zc and Cart, the lumped parameter models were fitted to Zin calculated from a distributed parameter model of the feline pulmonary vasculature. In addition, we assessed the concordance between the lumped parameter model estimates of Zc and Cart. The results indicate that no one model was superior; any of four models would be a reasonable choice. A four-element model was used to compare Zin measured at different phases of the respiratory cycle. Small differences in the impedance spectra were found that have not been previously reported. We conclude that lumped parameter models can be used to provide close approximations to Zin, to estimate Zc and Cart, and to provide a useful approach for statistical comparisons of impedance spectra.

scholarly journals Factors influencing stream water transit times in tropical montane watersheds

2015 ◽  
Vol 12 (10) ◽  
pp. 10975-11011 ◽  
Author(s):  
L. E. Muñoz-Villers ◽  
D. R. Geissert ◽  
F. Holwerda ◽  
J. J. McDonnell
Keyword(s):  
Land Use ◽  
Stream Water ◽  
Spatial Scales ◽  
Cloud Forest ◽  
Mean Transit Time ◽  
Field Measurements ◽  
Drainage Density ◽  
Soil Water Retention ◽  
Transit Times ◽  
Retention Characteristics

Abstract. Stream water mean transit time (MTT) is a fundamental hydrologic parameter that integrates the distribution of sources, flow paths and storages present in catchments. However, in the tropics little MTT work has been carried out, despite its usefulness for providing important information on watershed functioning at different spatial scales in (largely) ungauged basins. In particular, very few studies have quantified stream MTTs and related to catchment characteristics in tropical montane regions. Here we examined topographic, land use/cover and soil hydraulic controls on baseflow transit times for nested watersheds (0.1–34 km2) within a humid mountainous region, underlain by volcanic soil (Andisols) in central Veracruz (eastern Mexico). We used a 2 year record of bi-weekly isotopic composition of precipitation and stream baseflow data to estimate MTT. Land use/cover and topographic parameters (catchment area and form, drainage density, slope gradient and length) were derived from GIS analysis. Soil water retention characteristics, and depth and permeability of the soil–bedrock interface were obtained from intensive field measurements and laboratory analysis. Results showed that baseflow MTT ranged between 1.2 and 2.7 years across the 12 study catchments. Overall, MTTs across scales were mainly controlled by catchment slope and the permeability observed at the soil–bedrock interface. In association with topography, catchment form, land cover and the depth to the soil–bedrock interface were also identified as important features influencing baseflow MTTs. The greatest differences in MTTs were found at the smallest (0.1–1.5 km2) and the largest scales (14–34 km2). Interestingly, longest stream MTTs were found in the headwater cloud forest catchments.

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 Mean transit times in headwater catchments: insights from the Otway Ranges, Australia

2018 ◽  
Vol 22 (1) ◽  
pp. 635-653 ◽  
Author(s):  
William Howcroft ◽  
Ian Cartwright ◽  
Uwe Morgenstern
Keyword(s):  
Land Use ◽  
Major Ions ◽  
Stream Water ◽  
Shallow Groundwater ◽  
Drainage Density ◽  
Headwater Catchments ◽  
Southeastern Australia ◽  
Lumped Parameter ◽  
Transit Times ◽  
Major Ion Geochemistry

Abstract. Understanding the timescales of water flow through catchments and the sources 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 streamflow 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 in the Otway Ranges of southeastern Australia. 3H activities of stream water ranged from 0.20 to 2.14 TU, which are significantly lower than the annual average 3H activity of modern local rainfall, which is between 2.4 and 3.2 TU. The 3H activities of the stream water are lowest during low summer flows and increase with increasing streamflow. The concentrations of most major ions vary little with streamflow, which together with the low 3H activities imply that there is no significant direct input of recent rainfall at the streamflows sampled in this study. Instead, shallow younger water stores in the soils and regolith are most likely mobilised during the wetter months. MTTs vary from approximately 7 to 230 years. Despite uncertainties of several years in the MTTs that arise from having to assume an appropriate LPM, macroscopic mixing, and uncertainties in the 3H activities of rainfall, the conclusion that they range from years to decades is robust. Additionally, the relative differences in MTTs at different streamflows in the same catchment are estimated with more certainty. The MTTs in these and similar headwater catchments in southeastern Australia are longer than in many catchments globally. These differences may reflect the relatively low rainfall and high evapotranspiration rates in southeastern Australia compared with headwater catchments elsewhere. The long MTTs imply that there is a long-lived store of water in these catchments that can sustain the streams over drought periods lasting several years. However, the catchments are likely to be vulnerable to decadal changes in land use or climate. Additionally, there may be considerable delay in contaminants reaching the stream. An increase in nitrate and sulfate concentrations in several catchments at high streamflows may represent the input of contaminants through the shallow groundwater that contributes to streamflow during the wetter months. Poor correlations between 3H activities and catchment area, drainage density, land use, and average slope imply that the MTTs are not controlled by a single parameter but a variety of factors, including catchment geomorphology and the hydraulic properties of the soils and aquifers.

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.

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