Inversion of heat loss to obtain conductivity, density, and permeability at bottom-heated surfaces: the case of the hydrothermal system at Vulcano between 2019 and 2023

At hydrothermal systems, heat transfer across the final surface layer is driven by permeable convection and conduction, so that soil permeability and thermal conductivity play fundamental roles in controlling heat flux to the atmosphere. We build a Rayleigh-number driven heat transfer model for a bottom-heated surface that uses measurements of heat flux density (radiation and convection to the atmosphere in W/m2), surface temperature, and soil temperature to solve for soil conductivity, density, and permeability for such a bottom-heated surface. At Vulcano in 2019, we measured an ASTER-derived heat flux density of 240 ± 70 W/m2 and a difference between soil and surface temperature of 18 ± 6 °C. The surface layer is a 7.5 ± 2.5 cm thick case-hardened crust across which heat transfer is conduction dominated. We invert our heat transfer model using the temperature (T) gradient derived from a trench dug into the soil: T = − 49.7y2 + 113.6y + 35 (R2 = 0.9997), where y is depth in meters between the surface and 70 cm. The result is a conductivity for the case-hardened surface layer of 1.0 ± 0.3 W/(m K) and a density of 2440 ± 120 kg/m3. Below this case-hardened crust, heat transfer is dominated by permeable convection in a soil comprised of highly altered trachytic blocks in an ash matrix. Our model gives permeabilities of 1–19 × 10−10 m2 for this layer in 2019. In 2021, Vulcano entered a phase of unrest. Our model reveals that this was associated with an increase in permeability to 10−7 m2. However, by 2023 permeabilities had reverted to pre-unrest levels. Using simple measurements of surface and soil temperature, coupled with heat flux density from a satellite overpass, the model can be used as a basis to constrain heat transfer and to assess permeability at any hydrothermal system.