[1] Diamond Lake in Minnesota is covered every winter with ice and snow providing a modified thermal insulation between water and air. Autonomous temperature sensors, data loggers, were placed in this lake so that hourly measurements could be obtained from the snow-covered ice and water. The sensors that became frozen measured damped and delayed thermal response from the air-temperature fluctuation. Those sensors that were deeper within the snow-covered ice measured continuous, almost constant, temperature values near freezing. Several of them were within the liquid water and responded with a fluctuation of 24 h periods of amplitudes up to 0.2 C. Our analysis of the vertical temperature profiles suggested that the source of periodic water heating comes from the lake bottom. Because of the absence of daily temperature variations of the snow-covered ice, the influence of the airtemperature fluctuation can be ruled out. We attribute the heating process to the periodic inflow of groundwater to the lake and the cooling to the heat diffusion to the overlying ice cover. The periodic groundwater inflow is interpreted due to solid Earth tides, which cause periodic fluctuations of the groundwater pressure head.

Groundwater flow problems are mostly formulated by means of massbalance equation combined with Darcy's law. In this way, the flow is governed by a parabolic equation. To prevent inaccuracies which may result from this formulation, the Cattaneo approach can be utilized. The paper presents groundwater flow equation adopting the Cattaneo approach. In both 2D and 3D cases, the equation is of hyperbolic type and contains a constant known as relaxation time. The article focuses further on energy solutions defined on unbounded time interval. It is shown that under certain conditions, such solutions are oscillatory. The conditions sufficient to ensure the oscillatory solutions are derived. An upper bound for the oscillatory time is proved to be independent of the particular solution.

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A general theorem on the derivative of the volume average is formulated and proved. Conditions for the existence of the derivative are presented and discussed. This is done in order to give a better base to the theory of spatial averaging.