## 7 The Ground Thermal Gradient Model  
A further explanatory model for the late Holocene decline of tufa deposition rates and, more in general, for the increase/decrease of tufa deposition rates refers to the variations of thermal gradient in the bedrock by significant climate changes [56]. Due to the low thermal conductivity of bedrock [57; 58], major climatic changes to warmer conditions, such as the rapid increase in air temperature (up to several degrees) which occurred everywhere on the planet at the Late Pleistocene-Holocene transition [59],induces a significant thermal contrast between surface and ground and reverses thermal gradients in the deep limestone aquifers. With climate warming, the infiltration water, made highly acidic when crossing the soil due to the elevated partial pressure of biogenic CO\({}_{2}\) present therein, percolating through the progressively colder levels of the aquifer, induces a relevant dissolution of CaCO\({}_{3}\)[14, 60], higher than in normal conditions. At the emergence, because of the higher surface temperatures, the groundwater loses CO\({}_{2}\), becoming oversaturated with CaCO\({}_{3}\) and causing tufa deposition, even at a great distance from the spring; favored by the running water turbulence, photosynthetic activity of mosses and algae, and evaporation of spray droplets. Opposite effects, such as the deposition of dissolved carbonate in the upper bedrock layers and the emergence of spring waters undersaturated with CaCO\({}_{3}\), are expected to occur with major climatic changes to cold conditions. This could explain the occurrence of carbonate concretions in the bedrock fissures and tufa deposits and their erosion in the colder Quaternary stages [11, 56, 61, 62]. Changes in temperature of different amplitude ranging in timescales from years to millions of years have repeatedly affected the Earth's surface, inducing thermal variations in the ground of increasing depth, as a function of the magnitude and duration of the change [58]. With ground temperatures below 0 \({}^{\circ}\)C, groundwater freezes (permafrost) [63], preventing water circulation and the formation of calcareous tufa. Convective circulation in the groundwater may facilitate heat transfer, reducing the amplitude and duration of thermal differences between the upper and deeper levels of the bedrock [58]. However, in the case of massive limestones, the process mentioned above may not be significant since groundwater percolates down to the water table in a network of enlarged fissures, channels, and cavities within a much larger volume of almost or completely dry rock, with rock mass porosity values as low as 0.5% [64]. Furthermore, convective heat transfer may be reduced even in the saturated zone [56], considering that most of the phreatic water circulates at an extremely slow velocity in very narrow fractures and that the spacing between large fractures may reach several hundreds of meters [65]. As demonstrated by [PERSON] [66], water temperature records at the outlet of a fractured carbonate system during an annual cycle show two types of variations, slow variations over a small range, resulting from the thermal equilibrium between water and rock in the aquifer, and more rapid variations over a broader range, transmitted more quickly due to the inflow of water through fractures or karstic pipes. The heat exchange between rock mass and circulating water in the saturated zone is low, even though thermal disequilibrium may disappear over a long distance [67]. Disturbances of ground temperatures reaching depths down to several hundreds of meters were induced by the 100,000 years (glacialis-interglacialis) and the 41,000-21,000 (stadials-interstadials) climatic oscillations which occurred during the Quaternary [68]. Ultimately, the differences in temperature between the surface and the aquifer have the effect of increasing (warmer surface) or reducing (colder surface) the concentrations of dissolved calcium carbonate at the source and, consequently, the deposition rates of the calcareous tufa.