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Bobba, A. G. (1993). Mathematical models for saltwater intrusion in coastal aquifers. Water Resources Management, 7(1), 3–37.
Abstract: Flow of freshwater and saltwater intrusion in coastal aquifers has drawn the attention of many investigators. Several laboratory, as well as mathematical models have been developed to study the pattern of flow of groundwater in coastal aquifers. Mathematical models have wider range of application and are the concern of this paper. Due to the complex nature of the problem, each of these mathematical models are based on certain simplifying assumptions and approximations. This paper presents a critical review of various methods of solution which have been proposed. The validity of the results abtained and the limitations of these models are also discussed.
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Houben, G. (2018). Annotated translation of “Die Wasserversorgung einiger Nordseebäder [The water supply of some North Sea spas]” by Alexander Herzberg (1901). Hydrogeology Journal, 26(6), 1789–1799.
Abstract: The publication “The water supply of some North Sea spas” by Alexander Herzberg in 1901 is a cornerstone of coastal groundwater research. It was fundamental to the development of the Ghijben-Herzberg principle, which describes the hydrostatic equilibrium between fresh and saline groundwater. Due to its age and the language barrier, the paper is often cited but probably rarely read. Therefore, the original paper has been translated from German into English, accompanied by an introduction and notes explaining the historical context.
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Post, V. E. A., Houben, G. J., & van Engelen, J. (2018). What is the Ghijben-Herzberg principle and who formulated it? Hydrogeology Journal, 26(6), 1801–1807.
Abstract: It has been suggested in a number of historical notes that it was neither Willem Badon Ghijben nor Alexander Herzberg who formulated the famous principle now carrying their name, which relates the water-table elevation to the depth of the freshwater saltwater interface in coastal aquifers. In this paper, a systematic review of the literature pre-dating the publication of their work is presented. The aim is to establish to what extent these previous works captured the essence of the Ghijben-Herzberg principle, that is, the combination of a correct conceptual model of the hydrogeological conditions with a quantitative relationship. It was found that references to coastal fresh groundwater reserves can be traced back to Roman times, while the earliest detailed descriptions of a freshwater lens that could be found dates from the eighteenth century. The correct understanding of the hydrostatic equilibrium between fresh and salt groundwater is evident in works from the early nineteenth century. However, it was Badon Ghijben and Herzberg who combined this with the correct understanding of the groundwater conditions of a freshwater lens. It was further found that Herzberg had already recorded his findings in 1888 in a hand-written report, confirming speculation that such a report might exist.
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Schmittner, K. - E., & Giresse, P. (1999). The impact of atmospheric sodium on erodibility of clay in a coastal Mediterranean region. Environmental Geology, 37(3), 195–206.
Abstract: Heavy rainfalls, between 25 and 100 mm·h–1, were simulated on Pliocene/Quaternary sediments. To reproduce the heterogeneity of natural environments, 231 small plots of various sizes (between 2.5 and 3.5 m2; mean: about 3 m2) were used. The duration of all simulations was 1 h. We used water that had been collected during natural rainfall. The concentration of clay particles in the sheet wash depended upon the concentration of dissolved sodium in the wash (for about 42%) and of the sheet wash quantity (for about 37%). Under natural water conditions colloidal matter, like clay minerals, is charged negatively and therefore is destabilized by metal cations such as in the case of Na+. Results suggest that relatively higher concentrations of montmorrillonite were related to higher concentrations of sodium as opposed to illite and kaolinite. Microflakes of up to 25 μ were observed to vary between face-to-edge and face-to-face modes (competition between protons and other cations). The concentration of dissolved sodium (Na+) in the runoff water depends on water and sodium balances such as atmospheric input, infiltration, evaporation and surface water runoff. The reduction of vegetation cover increases the amount of salt and amorphous matter in/on the topsoil between heavy rainfall generations. The best predictor to explain montmorillonite, illite and kaolinite in % of mineral clay-sized matter in the surface water runoff (sheet wash) is the percentage of each clay mineral in the topsoil. As opposed to illite and kaolinite, more sheet wash indicate for montmorillonite relatively higher concentrations in the wash. The results of model simulations were confirmed on different field plots of about 1 ha and small catchments during natural heavy rainfall events. Models can also be used to understand and to better simulate sheet, rill and gully erosion, micropedimentation; and pedimentation.
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Siarkos, I., & Latinopoulos, P. (2016). Modeling seawater intrusion in overexploited aquifers in the absence of sufficient data: application to the aquifer of Nea Moudania, northern Greece. Hydrogeology J., 24, 2123–2141.
Abstract: In many coastal areas, overexploitation of groundwater resources has led both to the quantitative degradation of local aquifers and the deterioration of groundwater quality due to seawater intrusion. To investigate the behavior of coastal aquifers under these conditions, numerical modeling is usually implemented; however, the proper implementation of numerical models requires a large amount of data, which are often not available due to the time-consuming and costly process of obtaining them. In the present study, the investigation of the behavior of coastal aquifers under the lack of adequate data is
attempted by developing a methodological framework consisting of a series of numerical simulations: a steady-state, a false-transient and a transient simulation. The sequence and the connection between these simulations constitute the backbone of the whole procedure aimed at adjusting the various
model parameters, as well as obtaining the initial conditions for the transient simulation. The validity of the proposed methodology is tested through evaluation of the model calibration procedure and the estimation of the simulation errors (mean error, mean absolute error, root mean square error, mean relative error) using the case of Nea Moudania basin, northern Greece. Furthermore, a sensitivity analysis is performed in order to minimize the error estimates and thus to maximize the reliability of the models. The results of the whole procedure affirm the proper implementation of the developed methodology under specific conditions and assumptions due to the lack of sufficient data, while they give a clear picture of the aquifer’s quantitative and qualitative status.
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