This study presents the analytical solution for a radial advection-dispersion equation for a steady-state flow field in a horizontal aquifer caused by a constant rate injection from a well, including the mechanical dispersion and molecular diffusion terms in addition to the retardation and first-order attenuation under a Robin-type boundary condition at the well. The derived analytical solutions were compared with finely-meshed finite difference solutions in steady-state and periodic steady-state problems with typical parameters. The results suggest that the analytical solution is exactly derived and ready for application. Comparisons with analytical solutions ignoring molecular diffusion suggest that the derived analytical solution should be used when the product of the decay constant and the retardation factor and the ratio of injection rate to diffusion coefficient are small. Comparisons with analytical solutions with Dirichlet-type boundary conditions confirmed that Robintype boundary conditions should be used to exactly evaluate the concentration profile.

In the present study, we demonstrate how to perform, using quantum annealing, the singular value decomposition and the principal component analysis. Quantum annealing gives a way to find a ground state of a system, while the singular value decomposition requires the maximum eigenstate. The key idea is to transform the sign of the final Hamiltonian, and the maximum eigenstate is obtained by quantum annealing. Furthermore, the adiabatic time scale is obtained by the approximation focusing on the maximum eigenvalue.

The causes of land subsidence in Kawajima, Japan, have been investigated through data compilation and numerical modeling. Land subsidence has progressed despite a gradual increase in the hydraulic head in the long term. Taking into account the temporal changes and depth distribution of groundwater abstractions, the contraction of formations, and the complexity of the hydrogeological structures, it is proposed that agricultural groundwater use is one of the main triggers for land subsidence. A one-dimensional numerical simulator for coupled groundwater flow and soil deformation was developed with an evolutionary algorithm for model calibration. The calculated spatiotemporal changes in the past-maximum effective stress showed that plastic consolidation in the clayey layers progressed part by part every summer season resulting in long-term and gradual land subsidence under the same range of groundwater level fluctuations. The results also showed that the plastic deformation occurred in both the Holocene and Pleistocene sediments in the drought years, leading to significant subsidence. The model’s predictive performance showed good potential except for a structural prediction error after the Tohoku Earthquake in 2011. The scenario analysis indicated that management of the groundwater level in summer is one of the effective countermeasures in suppressing land subsidence caused by seasonal groundwater level fluctuations. These methodologies and findings can be used for groundwater management in similar cases around the world. Additional investigation is necessary on the influence of large earthquakes in deformation conditions in order to further improve the developed model.

<p>Land subsidence caused by seasonal fluctuation of groundwater level caused by agricultural groundwater use was numerically simulated in this study. In the study area, Kawajima, Saitama prefecture, Japan, the hydraulic head has been gradually increasing over time with seasonal fluctuations and the subsurface formations have repeated expansion and compaction. However, the land subsidence progressed because the compaction included the plastic deformation. In this study, vertically one-dimensional model to numerically simulate coupled groundwater flow and soil deformation in Kawajima was developed with modified cam-clay model. Because of the lack of subsurface information, it was difficult to set the physical properties such that the simulated subsidence and the observed subsidence are satisfactorily close to each other. This study applied a genetic algorithm in order to search the set of underground physical properties. The improved set of underground physical properties succeeded to reproduce the observed land subsidence in Kawajima.</p>

<p>This study tried to visualize the predictive uncertainty while predicting future land subsidence caused by the groundwater pumping. Because land subsidence modeling is highly uncertain, it is impossible to determine the distribution of subsurface physical property values uniquely. Therefore, we prepared various local optimal solutions through the inversion analysis with a genetic algorithm in order to visualize land subsidence prediction uncertainty. The inversion analysis was conducted using the long-term land subsidence monitoring data at Kawajima in the Kanto Plain, Japan. In this study site, the seasonal groundwater level fluctuations have caused plastic compaction in summer and elastic expansion in winter every year. Obtained multiple sets of subsurface properties were within the range of typical values in the existing literature and satisfactorily reproduced the observed subsidence, showing that the inversion analysis worked well. In addition, the groundwater level scenario analysis was conducted using obtained property sets. This revealed that the subsidences predicted for a sudden groundwater level drop and rapid recovery scenario are more volatile than the subsidences predicted for the stable scenario. This means that it is important to have multiple sets of subsurface properties to predict future land subsidence caused by unprecedented groundwater level fluctuations.</p>