Applied Mathematics & Information Sciences

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Soil properties and the position of illegal pumping wells can all be determined through the use of the groundwater level which, however, cannot be measured without the excavation of observation wells or the purchase of ground penetration radar. The former destroys terrain features, and the latter is expensive, aside from its limitations. This paper attempts to solve these problems by estimating groundwater levels economically via atmospheric conditions, and by collecting soil parameters near to the land’s surface. Firstly, the Penman-Monteith evaporation formula is explored to deduce the value of the embedded resistance ratio, which governs the involved water content, evaporation speed and, eventually, the groundwater level. Secondly, two theoretical models based on Darcy’s law are developed for predicting groundwater levels, one depending on a steady-state assumption and the other being identified as an analytical solution. To justify the first model, the time lapse required before achieving the steady state is estimated by solving numerically the air-liquid two-phase flow equations involving soil temperature variations. For efficiency, a special coordinate transformation is adopted to fix the spatial domains of all related numerical models between 0 and 1. The so-obtained numerical solutions not only testify to the accuracy of the newly developed theoretical models, but they also detect the interactions among air, water, evaporation, and temperature.

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