Residence time distributions of variable flow processes

Niemi, Antti J.

doi:10.1016/0020-708x(77)90026-6

Cited by 143 publications

(181 citation statements)

References 2 publications

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“…As per the outputs, the function that describes the distribution of the ages in the outflows, conditional to sampling time, is the travel time distribution conditional to the exit time. Following previous notations [Niemi, 1977;Botter et al, 2011], such distribution is denoted by p 0 out . Note that sampled ages can only be among those available in storage at the sampling time and the particle age's selection can differ at any sampling time, thus making the distributions a function of both t R and t. If the quantity OUT t ð Þp 0 out t R ; t ð Þ expresses, for each residence time, the amount of particles that leave the system via OUT(t), equation (2) becomes…”

Section: Methodsmentioning

confidence: 99%

Chloride circulation in a lowland catchment and the formulation of transport by travel time distributions

Benettin

Velde

Zee

et al. 2013

Water Resources Research

118

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[1] Travel times are fundamental catchment descriptors that blend key information about storage, geochemistry, flow pathways and sources of water into a coherent mathematical framework. Here we analyze travel time distributions (TTDs) (and related attributes) estimated on the basis of the extensive hydrochemical information available for the Hupsel Brook lowland catchment in the Netherlands. The relevance of the work is perceived to lie in the general importance of characterizing nonstationary TTDs to capture catchment transport properties, here chloride flux concentrations at the basin outlet. The relative roles of evapotranspiration, water storage dynamics, hydrologic pathways and mass sources/sinks are discussed. Different hydrochemical models are tested and ranked, providing compelling examples of the improved process understanding achieved through coupled calibration of flow and transport processes. The ability of the model to reproduce measured flux concentrations is shown to lie mostly in the description of nonstationarities of TTDs at multiple time scales, including short-term fluctuations induced by soil moisture dynamics in the root zone and long-term seasonal dynamics. Our results prove reliable and suggest, for instance, that drastically reducing fertilization loads for one or more years would not result in significant permanent decreases in average solute concentrations in the Hupsel runoff because of the long memory shown by the system. Through comparison of field and theoretical evidence, our results highlight, unambiguously, the basic transport mechanisms operating in the catchment at hand, with a view to general applications.

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Section: Methodsmentioning

confidence: 99%

Chloride circulation in a lowland catchment and the formulation of transport by travel time distributions

Benettin

Velde

Zee

et al. 2013

Water Resources Research

118

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“…Thus, one improvement that should be addressed is the adaptation of the approach to highly hydrodynamic environments, notably to karstic systems. This requires the use of time-varying transfer functions, which have been introduced in previous studies (Niemi 1977(Niemi , 1990Nir 1973;Ozyurt and Bayari 2005) but show restricted conditions for application in aquifers.…”

Section: Resultsmentioning

confidence: 99%

“…Some authors have expanded the convolution-based approach to model tracer transfer by introducing timevariant forms of analytical-model transfer functions (Niemi 1977(Niemi , 1990Nir 1973;Ozyurt and Bayari 2005). Whilst such methods were developed to study transfer processes in surface flow (Nir 1973), in groundwater (Ozyurt and Bayari 2005) or in industrial processes (Niemi 1977(Niemi , 1990, the required input data (variations of internal volume and/or input and output flows over the time) are difficult to obtain in groundwater domain.…”

Section: Introductionmentioning

confidence: 99%

“…Whilst such methods were developed to study transfer processes in surface flow (Nir 1973), in groundwater (Ozyurt and Bayari 2005) or in industrial processes (Niemi 1977(Niemi , 1990, the required input data (variations of internal volume and/or input and output flows over the time) are difficult to obtain in groundwater domain. Their use is therefore limited for hydrogeologic applications.…”

Section: Introductionmentioning

confidence: 99%

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Assessing groundwater quality trends in pumping wells using spatially varying transfer functions

et al. 2015

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When implementing remediation programs to mitigate diffuse-source contamination of aquifers, tools are required to anticipate if the measures are sufficient to meet groundwater quality objectives and, if so, in what time frame. Transfer function methods are an attractive approach, as they are easier to implement than numerical groundwater models. However, transfer function approaches as commonly applied in environmental tracer studies are limited to a homogenous input of solute across the catchment area and a unique transfer compartment. The objective of this study was to develop and test an original approach suitable for the transfer of spatially varying inputs across multiple compartments (e.g. unsaturated and saturated zone). The method makes use of a double convolution equation accounting for transfer across two compartments separately. The modified transfer function approach was applied to the Wohlenschwil aquifer (Switzerland), using a formulation of the exponential model of solute transfer for application to subareas of aquifer catchments. A minimum of information was required: (1) delimitation of the capture zone of the outlet of interest; (2) spatial distribution of historical and future pollution input within the capture zone; (3) contribution of each subarea of the recharge zone to the flow at the outlet; (4) transfer functions of the pollutant in the aquifer. A good fit to historical nitrate concentrations at the pumping well was obtained. This suggests that the modified transfer function approach is suitable to explore the effect of environmental projects on groundwater concentration trends, especially at an early screening stage.

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“…They were first introduced by Niemi (1977), then by Cornaton and Perrochet (2006), for example, and recently refined by Benettin et al (2015). Benettin et al (2015), in particular, related the backward concept to the residence time (or age), while the concept of travel time is both forward or backward.…”

Section: Definitions Of Age-ranked Quantitiesmentioning

confidence: 99%

Age-ranked hydrological budgets and a travel time description of catchment hydrology

Rigon

Bancheri

Green

2016

Hydrol. Earth Syst. Sci.

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Abstract. The theory of travel time and residence time distributions is reworked from the point of view of the hydrological storages and fluxes involved. The forward and backward travel time distribution functions are defined in terms of conditional probabilities. Previous approaches that used fixed travel time distributions are not consistent with our new derivation. We explain Niemi's formula and show how it can be interpreted as an expression of the Bayes theorem. Some connections between this theory and population theory are identified by introducing an expression which connects life expectancy with travel times. The theory can be applied to conservative solutes, including a method of estimating the storage selection functions. An example, based on the Nash hydrograph, illustrates some key aspects of the theory. Generalization to an arbitrary number of reservoirs is presented.

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Residence time distributions of variable flow processes

Cited by 143 publications

References 2 publications

Chloride circulation in a lowland catchment and the formulation of transport by travel time distributions

Chloride circulation in a lowland catchment and the formulation of transport by travel time distributions

Assessing groundwater quality trends in pumping wells using spatially varying transfer functions

Age-ranked hydrological budgets and a travel time description of catchment hydrology

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