A determination of the blowup solutions to the focusing, quintic NLS with mass equal to the mass of the soliton

Dodson, Benjamin

doi:10.2140/apde.2024.17.1693

This is the data used to create the published study of the same name published in the Journal of Hydrology in 2022 (10.1016/j.jconhyd.2022.104068). Shallow (<30 m) reducing groundwater commonly contains abundant dissolved arsenic (As) in Bangladesh. We hypothesize that dissolved As in iron (Fe)-rich groundwater discharging to rivers is trapped onto Fe(III)-oxyhydroxides which precipitate in shallow riverbank sediments under the influence of tidal fluctuations. Therefore, the goal of this study is to compare the calculated mass of sediment-bound As that would be sequestered from dissolved groundwater As that discharges through riverbanks of the Meghna River to the observed mass of As trapped within riverbank sediments. To calculate groundwater discharge, a Boussinesq aquifer analytical groundwater flow model was developed and constrained by cyclical seasonal fluctuations in hydraulic heads and river stages observed at three sites along a 13 km reach in central Bangladesh. At all sites, groundwater discharges to the river year-round but most of it passes through an intertidal zone created by ocean tides propagating upstream from the Bay of Bengal in the dry season. The annualized groundwater discharge per unit width at the three sites ranges from 173 to 891 m2/yr (average 540 m2/yr). Assuming that riverbanks have been stable since the Brahmaputra River avulsed far away from this area 200 years ago and dissolved As is completely trapped within riverbank sediments, the mass of accumulated sediment As can be calculated by multiplying groundwater discharge by ambient aquifer As concentrations measured in 1969 wells. Across all sites, the range of calculated sediment As concentrations in the riverbank is 78–849 mg/kg, which is higher than the observed concentrations (17–599 mg/kg). This discovery supports the hypothesis that the dissolved As in groundwater discharge to the river is sufficient to account for the observed buried deposits of As along riverbanks.

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