Interpretation of spring-water temperature variability based on continuous monitoring and numerical modelling of heat transport and water mixing: case study of Czarny Potok spring, Pieniny Mountains, southern Poland

A numerical model of heat conduction and water mixing was developed, enabling a quantitative description of water temperature variability at a spring outflow. The study examined the Czarny Potok spring, located in the Pieniny Mountains of southern Poland, which was the subject of a 4-year series of water temperature observations. The presented model describes the soil and water environment in the immediate vicinity of the spring, assuming that the spring water temperature is shaped by the mixing of water flowing through the shallow zone that experiences seasonal fluctuation and the deeper neutral zone. It was also assumed that the conductive heat flow in the tested medium is conditioned by seasonal heating and cooling of the land surface. The thermal diffusivity of the bedrock was calculated on the basis of the phase shift and the attenuation of thermal amplitude at different depths, based on long-term monitoring of soil temperature. The heat conduction and water mixing models enabled calculation of the water temperature at the outflow. The obtained results are close to the empirical spring water temperatures. The estimated mean error was 0.075 °C and the mean absolute error was 0.188 °C. The results of the calculations suggest that the tested spring is recharged primarily by water flowing through the seasonal fluctuation zone (75%), while the remaining 25% captures a deeper circulation system associated with the neutral zone.