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1

Sensitivity of optimized transient storage model parameters to spatial and temporal resolution

Wallis Steve, Manson Russell

Acta Geophysica

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2019

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Vol. 67, no. 3

951--960

EN

The transient storage model is a popular tool for modelling solute transport along rivers. Its use requires values for the velocity and shear flow dispersion coefficient in the main channel of the river together with two exchange rates between the main channel and transient storage zones, which surround the main channel. Currently, there is insufficient knowledge to enable these parameters to be predicted from the type of hydraulic variables that may typically be available. Hence, recourse is made to tracer experiments, which provide temporal solute concentration profiles that can be used to estimate the parameters by optimizing model output to observations. The paper explores the sensitivity of such parameters to the spatial and temporal resolutions used in the optimization of the model. Data from 25 tracer experiments covering a river flow rate range of 300–2250 L/s in a single reach of the river Brock in north-west England were used. The shear flow dispersion coefficient was found to be the most sensitive parameter; the velocity was found to be the least sensitive parameter. When averaged over all the experiments, mean percentage differences in parameter values between a coarse resolution case and a fine resolution case were of the order of 2% for the velocity, 70% for the shear flow dispersion coefficient and 30% and 20% for the two exchange rates. Since the shear flow dispersion coefficient was found to be small, both in numerical terms and in comparison with an estimate of the total dispersion in the reach, it is suggested that it may be viable to omit the shear flow dispersion term from the model.

2

A stem spacing‑based non‑dimensional model for predicting longitudinal dispersion in low‑density emergent vegetatio

Sonnenwald F., Stovin V., Guymer I.

Acta Geophysica

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2019

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Vol. 67, no. 3

943--949

EN

Predicting how pollutants disperse in vegetation is necessary to protect natural watercourses. This can be done using the one-dimensional advection dispersion equation, which requires estimates of longitudinal dispersion coefficients in vegetation. Dye tracing was used to obtain longitudinal dispersion coefficients in emergent artificial vegetation of different densities and stem diameters. Based on these results, a simple non-dimensional model, depending on velocity and stem spacing, was developed to predict the longitudinal dispersion coefficient in uniform emergent vegetation at low densities (solid volume fractions < 0.1). Predictions of the longitudinal dispersion coefficient from this simple model were compared with predictions from a more complex expression for a range of experimental data, including real vegetation. The simple model was found to predict correct order of magnitude dispersion coefficients and to perform as well as the more complex expression. The simple model requires fewer parameters and provides a robust engineering approximation.

3

Computer modelling of the dynamic system «porous medium – moisture – chemical substance» in the case of soil desalinization by rainfalls (a three-dimensional case)

Kozhushko Oksana D, Martyniuk Petro M.

Zeszyty Naukowe. Telekomunikacja i Elektronika / Uniwersytet Technologiczno-Przyrodniczy w Bydgoszczy

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2018

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nr 21

47--60

EN

Mathematical model of moisture transport taking into account variable porosity has been investigated numerically. Changes in porosity are caused by dissolution of chemical substances associated with soil skeleton. The finite element solution of the problem in the case of regular rainfall has been found. Program realization of the corresponding algorithms has been implemented in FreeFem++ computational environment. Numerical experiments have been carried out and the impact of rainfall on desalinization of soil with high concentration of salts in the solid component has been determined.

PL

Numerycznie badano model matematyczny transportu wilgoci o zmiennej porowatości. Zmiany porowatości są spowodowane rozpuszczaniem substancji chemicznych związanych ze szkieletem gruntu. Znaleziono numeryczne rozwiązanie problemu w przypadku regularnych opadów. Programowa realizacja odpowiednich algorytmów została zaimplementowana w środowisku obliczeniowym FreeFem++. Przeprowadzono eksperymenty numeryczne i określono wpływ opadów na odsalanie gruntu przy wysokim stężeniu soli w twardym komponencie.

4

Pollutant’s Horizontal Dispersion Along and Against Sinusoidally Varying Velocity from a Pulse Type Point Source

Singh M. K., Mahato N. K., Kumar N.

Acta Geophysica

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2015

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Vol. 63, no. 1

214--231

EN

An analytical solution of a two-dimensional advection diffusion equation with time dependent coefficients is obtained by using Laplace Integral Transformation Technique. The horizontal medium of solute transport is considered of semi-infinite extent along both the longitudinal and lateral directions. The input concentration is assumed at an intermediate position of the domain. It helps to evaluate concentration level along the flow as well as against the flow through one model only. The source of the input concentration is considered to be of pulse type. In the presence of the source, it is assumed to be decreasing very slowly with time, and just after the elimination of the source it is assumed to be zero. The dispersion coefficient and the advection parameter are considered directly proportional to each other. The analytical solution may be used to predict the solute concentration level with position and time in an open medium as well as in a porous medium. The effect of heterogeneity on the solute transport may also be predicted.

5

One-dimensional uniform and time varying solute dispersion along transient groundwater flow in a semi-infinite aquifer

Singh M., Ahamad S., Singh V.

Acta Geophysica

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2014

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Vol. 62, no. 4

872--892

EN

An analytical solution for the space-time variation of contaminant concentration in one-dimensional transient groundwater flow in a homogenous semi-infinite aquifer, subjected to time-dependent source contamination, is derived. The uniform and time varying dispersion along transient groundwater flow is investigated under two conditions. First, the flow velocity distribution in the aquifer is considered as a sinusoidally varying function, and second, the flow velocity distribution is treated as an exponentially increasing function of time. It is assumed that initially the aquifer is not solute free, so the initial background concentration is considered as an exponentially decreasing function of the space variable which is tending to zero at infinity. It is assumed that dispersion is directly proportional to the square of the velocity, noting that experimental observations indicate that dispersion is directly proportional to the velocity with a power ranging from 1 to 2. The analytical solution is illustrated using an example and may help benchmark numerical codes and solutions.

6

The numerical solution of the Advection-Dispersion Equation: A review of some basic principles

Wallis S.

Acta Geophysica

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2007

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Vol. 55, no. 1

85-94

EN

The simulation of solute transport in rivers is frequently based on numerical models of the Advection-Dispersion Equation. The construction of reliable computational schemes, however, is not necessarily easy. The paper reviews some of the most important issues in this regard, taking the finite volume method as the basis of the simulation, and compares the performance of several types of scheme for a simple case of the transport of a patch of solute along a uniform river. The results illustrate some typical (and well known) deficiencies of explicit schemes and compare the contrasting performance of implicit and semi-Lagrangian versions of the same schemes. It is concluded that the latter have several benefits over the other types of scheme.

7

Modelling solute transport in a small stream using DISCUS

Wallis S., Manson R.

Acta Geophysica Polonica

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2005

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Vol. 53, nr 4

501-515

EN

This paper describes the main features of the DISCUS model for one-dimensional advection-dispersion computations in rivers, and describes its application to a short reach of The Murray Burn (a small stream in Edinburgh). DISCUS was calibrated using tracer data and an optimisation technique that uses a genetic algorithm. The optimised dispersion coefficients were found to increase from 0.25 to 2 m2/s in the flow range 16-261 l/s. The model was validated using tracer data not used in the calibration stage. It appears that transient storage does not play a major role in the transport of solutes in the reach that was modeled.

8

Kinematic model of solute transport in stream networks: example with phosphate retention in Morsa Watershed, Norway

Wörman A., Klove B., Wachniew P.

Archives of Hydro-Engineering and Environmental Mechanics

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2004

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Vol. 51, nr 1

41-53

EN

A theoretical description of reactive solute transport in a network of stream channels is derived by convoluting unit solutions based on a physical representation of transport and topographical information of the distributions of solute load as well as pathways. The theory is applied to a generic analysis of the phosphate export in Morsa watershed due to the load from 620 individual households with a local wastewater treatment. Essential factors for the phosphate export is filtering of the water in stream-bed sediments through a distribution of hyporheic flow paths of various lengths. This generic study indicates that a significant portion of phosphate is retained in the hyporheic zones for a long time. The 90\% recovery time following a hypothetical remediation action in the households is expected to be in the order of one decade.

9

Characterisation of gypsum karst aquifers by heat and solute transport simulations

Birk S., Liedl R., Sauter M.

Acta Geologica Polonica

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2002

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Vol. 52, nr 1

23-29

EN

Environmental risks in gypsum karst areas such as geomechanical problems as a result of gypsum dissolution or the vulnerability of the aquifers due to the unretarded transport of pollutants are mainly determined by the karst conduit system. Therefore, in order to provide a reliable basis for risk assessment, an adequate hydrogeological characterisation of the conduit system is required. A newly developed modelling tool is presented, which has been designed to support the characterisation of the conduit system of gypsum karst aquifers by simulating short-term fluctuations of solute concentrations and temperatures of the spring water. Both solute concentration and temperature of the spring water depend on the geometric and hydraulic properties of the conduit system. If only one of these parameters is analysed a unique identification of the structure of the conduit system may not always be obtained. Unsteadystate simulations of both heat and solute transport, however, show that different conduit systems, which are equivalent with respect to spring of one parameter, can be distinguished by taking into account a second parameter.