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

Inversion of heat loss to obtain conductivity, density and permeability at bottom-heated surfaces: The case of hydrothermal system at Vulcano between 2019 and 2023 | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Inversion of heat loss to obtain conductivity, density and permeability at bottom-heated surfaces: The case of hydrothermal system at Vulcano between 2019 and 2023 Andrew Harris, Sophie Pailot-Bonnétat This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3940847/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 20 May, 2024 Read the published version in Bulletin of Volcanology → Version 1 posted 5 You are reading this latest preprint version Abstract At hydrothermal systems, heat transfer across the final surface layer is driven by permeable convection and conduction, so that permeability and conductivity play fundamental roles in controlling the 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. 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 by using the derived temperature (T) gradient of 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 layer of 1.0 ± 0.3 W/(m K) and density of 2440 ± 120 kg/m 3 . Below the case harded layer heat transfer is dominated by permeable convection, and a soil comprised of highly altered trachytic blocks in an ash matrix. Our model gives permeabilities of 1–19 × 10 − 10 m² of 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. Heat flux Hydrothermal system permeability conductivity Vulcano ASTER Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Introduction At vapor-dominated hydrothermal systems ascending vapor cools and boils near the surface (White et al., 1971 ). In such a system, vapor ascends the geothermal “heat pipe” (White et al., 1971 ) to condense at the 100°C isotherm (McGuiness et al., 1993). Upon condensation, liquid water descends and heat generated by condensation is transferred to the surface by permeable convection and conduction (e.g., Aubert et al., 2008 ; Hochstein & Bromley, 2005 ; Hurwitz et al., 2012 ). Heat is then transferred from the surface to the atmosphere by radiation and free-or-forced convection (e.g., Sekioka & Yuhara, 1974 ; Matsushima et al., 2003 ; Harris, 2013 ). The heat transfer process from the primary source (the deep magmatic system) through the hydrothermal system to the surface is thus driven by permeable convection and conduction (Hardee, 1984). As a result rock permeability and thermal conductivity play fundamental roles in transfering heat through the system (e.g., Tanaka et al., 2017; Favorito et al., 2021 ; Stissi et al., 2021 ). This is the case for the hydrothermal system beneath the Fossa crater of Vulcano (Aeolian Islands, Italy). At the Fossa, magmatic vapor ascends from a source around 2000–3000 m below the crater (Ferrucci et al., 1991 ) to mix with meteoric and marine fluids in a biphase to vapor-monophase system (e.g., Carapezza et al., 1981 ; Chiodini & Cioni, 1995; Nuccio et al. 1999 ) at a depth of 500–1500 m (Alparone et al., 2010 ). Efficiency of heat flow up the “heat pipe” above the mixing zone is strongly dependent on permeability (Diliberto, 2011 , 2017 ; Harris et al., 2012 ), especially over the last few hundred meters of ascent (Nuccio et al., 1999 ). Water condensing near-surface at the 100°C isotherm generates heat that creates a surface thermal anomaly at the head of the heat pipe (Chiodini et al., 2005 ; Aubert et al., 2019). The heat pipe is tightly culminated by self-sealing, creating a high permeability zone where mass and heat fluxes are concentrated (Harris & Maciejewski, 2000 ; Chiodini et al., 2005 ; Mannini et al., 2019 ). In April 2019 we set up an experiment in the Vulcano Fossa crater that allowed us to measure the surface and soil temperatures at the head of the heat pipe, simultaneous with heat flux derived from ASTER (Advanced Spaceborne Thermal Emission and Reflection Radiometer). This allows us to assess the morphological and thermal conditions of the thermal boundary layer between the heat source (condensation) and sink (surface heat losses) and construct an open, cascading system for heat transfer from the source to the sink. Inversion of the model allows the rock thermodynamic properties (conductivity, density and permeability) to be quantified. Given continuity in these measurements through 2023 (Pailot-Bonnétat & Harris, 2023) allows us to track changes in permeability before, during and after the period of unrest that began in 2021. Models and Methods Heat transfer model Following McGuiness et al. (1993), we set up a heat transfer model whereby ascending vapor arriving at the 100°C isotherm condenses to generate heat. Heat generated by condensation is then transferred to the surface by permeable convection and conduction (Hochstein & Bromley, 2005 ; Hurwitz et al., 2012 ). This sets up a thermal gradient that declines over a typical height of 1–10 m from 100°C to ≤ 30–50°C near the surface (e.g., Dobson et al., 2003 ; Chiodini et al., 2005 ; Aubert et al., 2018). We adapt this model to the near-surface morphology of the Vulcano Fossa, as defined from a trench dug in June 2021. This revealed that the thermal gradient at the Fossa crosses two main rock layers: a lower zone of altered breccia and a cemented surface layer (Fig. 1 ). The immediate sub-surface (rock layer 1, Fig. 1 ) is unconsolidated and comprises altered cm-blocks of trachyte in a sand-ash matrix (Fig. 2 ). Below 60 cm mineralization is apparent, and blocks are altered to clay. Discontinuous layers of thin, hard, cemented duripan can also be found below 70 cm (Fig. 2 ). The surface layer is a 5-to-10 cm-thick case-hardened crust of cemented silt, sand and trachytic blocks (rock layer 2, Fig. 1 ). Case hardened crusts are “hard, resilient crusts on the surfaces of boulders and outcrops of soft, porous rock caused through the filling of voids with natural cement” (Goudie, 2000 ; Viles and Goudie, 2004 ). Such crusts have been described on the Keanakakoi deposits of Kilauea, where they result from cementing of the silt-sand matrix due to silicate and sulfate mineral deposition from passage of acid gasses and fluids (Malin et al., 1983 ); as is the case at Vulcano. Such cemented layers self-seal the system, where particle agglutination and pore filling with minerals reduces air and water circulation (Rammlmair, 2002 ). Such cemented layers are associated with high thermal conductivities (Piqueux & Christensen, 2009 ). Thus, following Hardee (1984) and Aubert et al. (1998), our model considers heat transfer (τ) across the upper cemented layer (rock layer 2) to be dominated by conduction, with τ across lower unconsolidated layer (rock layer 1) being dominated by permeable convection (Fig. 3 a). The profile of air temperature in the first meter above the surface reveals a thermal boundary layer of height 40 cm (Fig. 2 ). Across the boundary layer, air temperature decreases from 34.5 to 32.5°C, i.e., 0.5°C per meter, to stabilize at between 32 and 32.5°C. Following Incropora et al. ( 2017 ), velocity of the fluid at the base of the boundary layer will be zero and air temperature will equal surface temperature. Below the surface, the temperature profile has the form T = -49.7y² + 113.6y + 35 (R² = 0.9997) (Fig. 2 ), which projects the 100°C isotherm to be at a depth of 1.05 ± 0.05 m. Based on this morphological system, we build a cascading system where heat transfer from the source (M in , condensation of ascending vapor) to the sink (M out , radiation and convection to the atmosphere) is described by permeable convection across rock layer 1 of height H. Instead, heat transfer across rock layer 2, of height h, is by conduction (Fig. 3 b). Following Hardee (1984), permeable convection (M conv in W m -2 ) can be described by: M conv = h c (T 100 -T b ) (1) in which T 100 is boiling temperature, T b is the temperature at the interface of rock layers 1 and 2, and h c is the convective heat transfer coefficient (Fig. 3 b). Following Holman (1994), the convective heat transfer coefficient can be related to the Nusselt Number (Nu) in: h c = (k Nu / H) (2) where k is rock thermal conductivity. For a bottom heated surface with a colder top surface (Incropera et al., 2017), Nu = 0.54 Ra 1/4 (10 4 ≲ Ra ≲ 10 7 ) (3a) Nu = 0.15 Ra 1/3 (10 7 ≲ Ra ≲ 10 11 ) (3b) Ra being the Rayleigh Number, written in terms of permeability (κ) is (cf. Wicky & Hauck, 2020 ): Ra = [ρ² c a g β H (T 100 - T b ) κ] / [µ k] (4) Here, g is acceleration due to gravity, ρ is the density of the rock, c a and µ are the specific heat capacity and dynamic viscosity of steam, and β is the coefficient of thermal expansion [i.e., 1/T, with T being (T 100 + T b )/2]. In its most simple form, conduction (M cond in W m -2 ) can be described using Fourier’s Law: M cond = k (ΔT/h) (5) in which ΔT is T b -T surf , T surf being the surface temperature (Fig. 3 b). In Eq. (5), conductivity can be related to rock density using thermal diffusivity (α) and specific heat capacity (c p ) through: α = k / (ρ c p ) (6) We assume that all heat convected across rock layer 1 is conducted through rock layer 2 to be lost from the surface (Fig. 3 a), so that M in = M conv ≈ M cond = M out . Now, given a measurement of the surface leaving heat flux (M out ), temperatures T surf , T b and T 100 , and the thermodynamic properties of steam, the system can be inverted to solve for the three key thermodynamic properties of the rock: conductivity, density of layer 2 and permeability of layer 1 (Fig. 3 c). Thus, to solve for k, ρ and κ, we thus measure M out , T surf and T b (Fig. 3 b), and use c a of 4190 J/(kg K) and 3.77 × 10 − 4 Pa s for µ (for steam at 75°C, https://www.ski-gmbh.com/swa/tools/steam ). Input measurements Heat loss data from the surface to the atmosphere (M out = M atmosphere , Fig. 3 ) were obtained from thermal infrared images (10.95–11.65 µm, 90 × 90 pixel) acquired by ASTER. The surface temperatures are taken from the AST_08 products in which emissivity corrections and atmospheric corrections have already been performed automatically. Heat is lost by radiation (M rad ) and forced convection (M conv ) which can be described by Fig. 3 : M force = h a (T max -T ambient ) (7) M rad = σ ε (T max 4 -T ambient 4 ) (8) in which T max is the maximum temperature of the thermally anomalous pixels in La Fossa crater, T ambient is the average temperature of the inactive Vulcanello cone at the northern end of Vulcano, h a is the atmospheric convective heat transfer coefficient (35 W m -2 K -1 following Matsushima et al. ( 2003 ), σ is the Stefan-Boltzmann constant, and ε is the emissivity of the ground surface (0.98). On 29 April 2019 at 22h30 (CET), three thermally anomalous pixels were found over the Fossa. The atmospherically corrected temperatures (T surf = 17.9, 18.4 and 16.7°C) were converted to radiative and convective heat losses (M rad and M force ) using ambient temperatures (T a ) of 11.2, 11.4 and 12.6°C (Fig. 3 b) following the approach of Mannini et al. ( 2019 ). This gave M rad of 30 ± 10 W/m² and M force of 210 ± 60 W/m², for a total heat loss from the bottom heated surface (M out , Fig. 3 a) of 240 ± 70 W/m². A total of 11 field campaigns were made following the April 2019 experiment with 30 near-simultaneous ASTER overpasses. The data for each overpass, and calculated M out are given in Table 1 . We used the data from the closest overpass in time to our field campaigns as input in the inversion model. Table 1 List of available ASTER night-time overpasses close in time to our field campaigns with T max and T ambient used to calculate M rad , M force and M out (Fig. 3 ). Date T max (°C) T ambient (°C) M force (W/m²) M rad (W/m²) M out (W/m²) 04/29/19 18.4 11.4 210 30 240 01/30/20 18.6 9.9 303 46 349 10/28/20 20.6 12.6 279 43 322 02/17/21 17.4 10.9 225 34 259 03/12/21 19.3 11.2 282 43 325 04/06/21 18.3 15.5 96 15 110 04/13/21 19.1 13.0 211 32 243 05/08/21 24.1 17.2 241 39 280 05/24/21 24.4 19.8 159 26 184 05/31/21 24.6 19.8 166 27 193 06/25/21 35.8 26.9 312 56 367 07/11/21 32.6 27.4 182 32 214 07/18/21 30.8 24.2 231 40 270 07/27/21 34.1 26.9 251 45 296 08/12/21 35.8 27.9 276 50 326 08/19/21 37.4 27.7 339 61 400 08/28/21 33.4 26.9 225 40 265 09/13/21 32.7 23.4 323 56 379 09/20/21 32.3 22.7 333 58 391 09/29/21 32.0 22.9 318 55 373 12/01/21 26.7 15.2 400 65 465 01/19/22 23.0 9.3 478 73 551 01/26/22 18.7 6.7 418 62 480 02/04/22 24.8 11.6 461 72 534 03/08/22 18.0 7.7 359 53 412 03/15/22 21.1 10.7 364 56 420 03/24/22 23.4 10.4 453 70 523 09/07/22 34.9 23.7 390 68 458 01/12/23 20.8 12.6 286 44 331 06/26/23 30.7 25.4 182 32 214 To provide data for T surf and T b we completed temperature measurements of the suface with a thermal infrared thermometer and obtained temperature at a depth of 10 cm using a k-type thermocouple inserted into holes drilled through the surface layer (rock layer 2, Fig. 1 ). Measurements were made every 5 m along a 50 m transect that traversed the eastern edge of the hydrothermally heated area (Fig. 4 ). On the day of the ASTER acquisition, 29 April 2019, this gives a T surf of 31 ± 5°C and T b of 30 ± 4°C for the non-heated zone, so that ΔT ≈ 0. However, in the thermal zone we have T surf of 37 ± 4°C and T b of 55 ± 10°C, so that ΔT = 18 ± 6°C. All temperature profiles of T surf and T b collected between 2019 and 2024 are given in Fig. 5 , and temperature data are summaried in Table 2 . Table 2 Mean T surf and T b (with standard deviation as error) collected during the field campaigns of 2019–2023 for the cold and hot zones along the 50 m transect (Fig. 4 ). COLD ZONE HOT ZONE Date T surf ±σ T b ±σ T surf ±σ T b ±σ 04/29/19 31 5 30 4 37 4 55 10 01/31/20 26 2 24 2 30 4 63 17 10/19/20 25 2 24 1 32 4 48 14 03/19/21 10 2 18 3 15 3 46 19 06/14/21 38 6 35 1 34 7 60 14 09/18/21 45 3 49 21 51 4 81 11 01/12/22 15 3 29 14 26 6 65 19 05/29/22 31 2 38 7 36 2 67 15 09/07/22 44 2 40 10 54 1 66 14 03/13/23 31 5 28 10 39 4 54 18 06/26/23 31 2 36 6 37 3 57 15 Results: Inversion of the heat transfer model Thermal conductivity and density, April 2019 Using the value of M out (240 ± 70 W/m²) for M cond in Eq. (5), with the ΔT of 18 ± 6°C (Fig. 6 ) and h of 7.5 ± 2.5 cm, as measured on April 29, 2019, we obtain a thermal conductivity of 1.0 ± 0.3 W/(m K). This compares with a thermal conductivity of 0.8 ± 0.25 W/(m K) calculated for Vulcano by Aubert et al. ( 2008 ). To obtain density of layer 2 (Fig. 1 ), we thus use a thermal conductivity of 1.0 ± 0.3 W/(m K) and rearrange Eq. (6). To solve, we use a rock thermal diffusivity of 0.4 ± 0.13 × 10 − 6 m²/s, these being the values found for thermal ground at New Zealand’s Wairakei hydrothermal system by Hochstein and Bromley ( 2005 ), and 1025 ± 25 J/(kg K) for the specific heat capacity [after Hardee (1982) and Stissi et al. ( 2021 )]. This gives a density of 2440 ± 120 kg/m 3 for rock layer 2, which compares with a dense rock density for trachyte of 2700 kg/m 3 (Prival et al., 2022 ) and a bulk density for debris flows at Vulcano comprising the same components as rock layer 2 of 1950 kg/m 3 (Ferrucci et al., 2005 ). Permeabillity, April 2019 The measurements along the transect on April 29, 2019 gave T b of 55 ± 10°C (Fig. 5 ), and measurements in the trench show that the depth to the 100°C isotherm (H) was 1.0 ± 0.1 m (Fig. 2 ). Using these values with M conv of 240 ± 70 W/m² and thermal conductivity of 1.0 ± 0.3 W/(m K) in rearranged forms of Equations (1), (2) and (3) gives a convective heat transfer coefficient of 5.3 ± 2.2 W/(m² K), and a Nusselt number of 5 ± 1 and Rayleigh number of 9.5 ± 6.7 × 10 3 . Now, using these values in a re-arranged form of Eq. (4), with a density of 2440 ± 120 kg/m 3 , we obtain a permeability for layer 1 (Fig. 1 ) of between 1.1 × 10 –10 and 1.9 × 10 –11 m². This permeability range spans that used by Tanaka et al. (2017), i.e., 5.0 × 10 –10 m², to numerically model heat flux in the “conduit” zone feeding the hydrothermal system of Mt. Tokachidake (Japan). However, our premeability is a little higher than those derived from numerical simulations of heat and mass transfer at Vulcano by Stissi et al. ( 2021 ), i.e., 1.25–8.2 × 10 –12 m². This is no doubt due to the model of Stissi et al. ( 2021 ) considering depths down to -1500 m, whereas our model is for the final meter of heat transfer. At depth, argillic alteration and sealing will serve to decrease permeability (Dobson et al., 2003 ; Julia et al., 2014 ), so that the median permeability for the heat pipe above the mixing zone at Vulcano is likely of the order of 10 –11 m², being 10 –12 m² at depth and 10 –10 m² near-surface. Discussion: Permeability evolution at Vulcano, 2019–2023 Vulcano entered a new phase of unrest in 2021, which culiminated in an increase in T b at our control site from 25°C on September 11 to 69°C by October 7 (Pailot-Bonnétat & Harris, 2024 ). This was coupled with an increase in the area of the thermal anomaly recorded in ASTER data from 7 to 35 pixels. As a result, the total heat flux increased from baseline levels of ~ 40 MW in March 2021 to a peak of 120 MW in March 2022 (Pailot-Bonnétat et al., 2023 ). Our ASTER-derived heat fluxes between April 2019 and June 2023, and spanning the unrest, are given in Fig. 6 a and field-measured ΔT in Fig. 6 b, with derived heat transfer coefficient and permeability in Figs. 6 c and 6 d. We see an increase in heat flux from 350 W/m² in 2021 to almost 550 W/m² by the middle of 2022 (Fig. 6 a), with ΔT peaking at the same time (Fig. 6 b). In parallel with this, the efficiency of heat transfer, as described by h c , increased from a relatively stable level of ~ 5 W/(m² K) from 2019 through the first half of 2021, to ~ 20 W/(m² K) by September 2021 (Fig. 6 c). This was matched by a peak in permeability at around 10 − 7 m², compared with 2019–2021 levels of 10 − 9 to 10 –10 (Fig. 6 d). All parameters began to decline during 2022 to reach pre-unrest levels by 2023 (Fig. 6 ). Auippa et al. (2022) ascribes the onset of unrest to the presence of ~ 3 × 10 6 m 3 mafic magma at a depth of 4–5 km, with this magma probably being injected around the beginning of 2021 when the first signs of unrest were recorded (Pailot-Bonnétat et al., 2023 ). Sealed-zones failed in September 2021, when a widespread increase in permeability caused expansion in the area of soil degassing (Federico et al., 2023 ; Pailot-Bonnétat et al., 2023 ). At this point we record an increase in permeability of the upper portion of the heat pipe, which increased the efficiency of the heat transfer process (Fig. 6 ). By the second half of 2022 our two main metrics of unrest, M out (Fig. 6 a) and ΔT (Fig. 6 b), were turning around. Application of our heat transfer model suggests that this was associated with re-sealing to bring permeabilities (Fig. 6 d), and hence the heat transfer coefficient (Fig. 6 c), back to the pre-unrest levels. Conclusions We show here how simple field-based temperature measurements, coupled with derivation of heat flux density from near-simultaneous overpasses of satellites carrying infrared sensors, can be used to derive and track permeability. For near-surface heat transfer at hydrothermal system, permeability is the main driver controlling heat fluxes across a heat pipe extending between a fluid mixing zone and the surface. To derive and track permeability, we need to build a Rayleigh-number driven heat transfer model for a bottom-heated surface. At Vulcano, we find that the model allows us to track changes in permeability that drive variations in heat flux density and soil temperatures during transition from baseline to unrest levels, and back again. While the order of magnitude of permeabilities obtained here can be used for modelling (e.g., Tanaka et al., 2017; Favorito et al., 2021 ; Stissi et al., 2021 ), the methodology can be used to assess permeabilities at other hydrothermal systems, and the heat transfer model can be used as a basis to fully constrain heat flux from source to sink at a hydrothermal system. Declarations Acknowledgments We thank Mike Ramsey (University of Pittsburgh) for help with triggering the ASTER Urgent Response Protocol for timely image provision. Guillaume Boudoire, Roxane Buso, Iole Serena Diliberto, Alessando Gattuso, Fausto Grassa, Nicolas Levillayer, Stefano Mannini, Victoria Rafflin, Luca Teray, and Benjamin Van Wyk de Vries are thanked for field implementation and science discussions. We are most grateful to INGV-Palermo for making the facilities at the Carapezza Center on the island of Vulcano open and available to us. Finally, working through the Covid-19 global pandemic would not have been possible without the help and support of Tanino at the Casa Genovese (Vulcano), Maurizio at "La Forgia" (Vulcano), Manfreddi at La Giarra (Vulcano), all at the Filadelfia (Lipari), the “Faraglione” bar, and the Carabinieri of both Vulcano and Lipari. Funding This work was financed by the Agence National de la Recherche (ANR) through the project DIRE (Program: CES 04 Innovations scientifques et technologiques pour accompagner la transition écologique: project no.: ANR-19-CE04-0014–01) and Labex Clervolc project no. 2019–22. This is contribution no. XXX of the ClerVolc program of the International Research Center for Disaster Sciences and Sustainable Development of the University of Clermont Auvergne. Conflicts of interest/Competing interests Not applicable Availability of data and material All data sets are freely available as Supplementary Information, as part of a spreadsheet in which the model is also set-up. 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Geological Society of America Bulletin , 94 (10), 1148. https://doi.org/10.1130/0016-7606(1983)942.0.CO;2 Mannini, S., Harris, A. J. L., Jessop, D. E., Chevrel, M. O., & Ramsey, M. S. (2019). Combining Ground- and ASTER-Based Thermal Measurements to Constrain Fumarole Field Heat Budgets: The Case of Vulcano Fossa 2000–2019. Geophysical Research Letters , 46 (21), 11868–11877. https://doi.org/10.1029/2019GL084013 Matsushima, N., Kazahaya, K., Saito, G., & Shinohara, H. (2003). Mass and heat flux of volcanic gas discharging from the summit crater of Iwodake volcano, Satsuma-Iwojima, Japan, during 1996-1999. Journal of Volcanology and Geothermal Research , 126 (3–4), 285–301. https://doi.org/10.1016/S0377-0273(03)00152-5 Mcguinness, M. J., Blakeley, M., Pruess, K., & O’sullivan, M. J. (1993). Geothermal Heat Pipe Stability: Solution Selection by Upstreaming and Boundary Conditions. Transport in Porous Media , 11 , 71–71. Nuccio, P. M., Paonita, A., & Sortino, F. (1999). Geochemical modeling of mixing between magmatic and hydrothermal gases: the case of Vulcano Island, Italy . Earth and Planetary Science Letters (Vol. 167). Pailot-Bonnétat, S., & Harris, A. J. L. (2024). A Thermal Record for Unrest at Vulcano 2020–2022: In Situ Meteorological Data and Soil Temperature Recorded at High Temporal Resolution. Bulletin of Volcanology , 86 (2), 13. https://doi.org/10.1007/s00445-023-01696-3 Pailot-Bonnétat, S., Rafflin, V., Harris, A., Diliberto, I. S., Ganci, G., Bilotta, G., et al. (2023, December 1). Anatomy of thermal unrest at a hydrothermal system: case study of the 2021–2022 crisis at Vulcano. Earth, Planets and Space . Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1186/s40623-023-01913-5 Piqueux, S., & Christensen, P. R. (2009). A model of thermal conductivity for planetary soils: 2. Theory for cemented soils. Journal of Geophysical Research: Planets , 114 (9). https://doi.org/10.1029/2008JE003309 Prival, J.-M., Harris, A. J. L., Zanella, E., Test, C. R., Gurioli, L., Chevrel, O., & Biren, J. (2022). Emplacement dynamics of a crystal-rich, highly viscous trachytic flow of the Sancy stratovolcano, France. GSA Bulletin , 135 (7–8), 2057–2074. https://doi.org/10.1130/B36415.1 Rammlmair, D. (2002). Hard pan formation on mining residuals. In B. J. Merkel, B. Planer-Friedrich, & C. Wolkersdorfer (Eds.), Uranium in the Aquatic Environment (pp. 173–182). Berlin, Heidelberg: Springer Berlin Heidelberg. Sekioka, M., & Yuhara, K. (1974). Heat flux estimation in geothermal areas based on the heat balance of the ground surface. Journal of Geophysical Research , 79 (14), 2053–2058. https://doi.org/10.1029/jb079i014p02053 Stissi, S. C., Napoli, R., Currenti, G., Afanasyev, A., & Montegrossi, G. (2021). Influence of permeability on the hydrothermal system at Vulcano Island (Italy): inferences from numerical simulations. Earth, Planets and Space , 73 (1). https://doi.org/10.1186/s40623-021-01515-z Tanaka, R., Hashimoto, T., Matsushima, N., & Ishido, T. (2018). Contention between supply of hydrothermal fluid and conduit obstruction: inferences from numerical simulations. Earth, Planets and Space , 70 (1). https://doi.org/10.1186/s40623-018-0840-6 Viles, H. A., & Goudie, A. S. (2004). Biofilms and case hardening on sandstones from Al-Quwayra, Jordan. Earth Surface Processes and Landforms , 29 (12), 1473–1485. https://doi.org/10.1002/esp.1134 White, D. E., Muffler, J. P., & Truesdell, A. H. (1971). Vapor-Dominated Hydrothermal Systems Compared with Hot-Water Systems. Economic Geology , 66 , 75–97. Wicky, J., & Hauck, C. (2020). Air Convection in the Active Layer of Rock Glaciers. Frontiers in Earth Science , 8 . https://doi.org/10.3389/feart.2020.00335 Cite Share Download PDF Status: Published Journal Publication published 20 May, 2024 Read the published version in Bulletin of Volcanology → Version 1 posted Editorial decision: Moderate revision (possibly re-reviewed) 03 Apr, 2024 Reviewers agreed at journal 03 Mar, 2024 Editor assigned by journal 22 Feb, 2024 Editor invited by journal 20 Feb, 2024 First submitted to journal 07 Feb, 2024 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-3940847","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":276090224,"identity":"4f6de5c0-6bc7-449f-8036-c39b056ffcb8","order_by":0,"name":"Andrew Harris","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA20lEQVRIie3OIQvCQBTA8XccLDlWL7mvcMOoH2ZD0CKWFYNhIKzZNyb6FRRhefJAyzQvGPQbbG0GxTswmG6zGe4f3rvy4x2ATvefcTlcOTKYyUVuv5BcLsrbEyBhC2Ili7SsQphayfl+eKzRtgJqlCrCrkc/jkPw2WXM0UzRiTJKI+WZYtKjZgpekBuAJEUXMguVwpbkKchGkMNjha4trigJl4QIshUkMwN0eRNxipFPli/m7eTHOsexs8MG0i2Ge6jzgbfODVrV877dPS3U5BP7ercCOp1Op1P2BmRpSNXXS93EAAAAAElFTkSuQmCC","orcid":"","institution":"Universite Clermont Auvergne","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"Andrew","middleName":"","lastName":"Harris","suffix":""},{"id":276090225,"identity":"26d51818-6363-4b51-b502-5d849fe01eac","order_by":1,"name":"Sophie Pailot-Bonnétat","email":"","orcid":"https://orcid.org/0000-0003-4653-2187","institution":"Université Clermont Auvergne - Campus des Cézeaux: Universite Clermont Auvergne - Campus des Cezeaux","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Sophie","middleName":"","lastName":"Pailot-Bonnétat","suffix":""}],"badges":[],"createdAt":"2024-02-08 18:49:44","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-3940847/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-3940847/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s00445-024-01746-4","type":"published","date":"2024-05-20T09:07:55+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":52106159,"identity":"d68d7086-2b1a-455e-ab55-acb4a3616092","added_by":"auto","created_at":"2024-03-06 19:36:11","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":3825645,"visible":true,"origin":"","legend":"\u003cp\u003e75-cm-deep trench dug in the heated ground of the Vulcano Fossa fumarole field. Rock layer [2] is a case-hardened crust (c) of cemented silt, sand and trachytic blocks (t). Rock layer [1] is a breccia of altered trachytic blocks (a) in a sand-rich matrix with discontinuous duripan (d) layers at depth\u003c/p\u003e","description":"","filename":"Figure1.png","url":"https://assets-eu.researchsquare.com/files/rs-3940847/v1/07c5ddf827d205217505eac7.png"},{"id":52106149,"identity":"6d1cb59b-b067-455c-89c8-0874c4f0df94","added_by":"auto","created_at":"2024-03-06 19:36:09","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":3390090,"visible":true,"origin":"","legend":"\u003cp\u003eLog, air temperature and ground temperature profiles of the trench of Fig. 1\u003c/p\u003e","description":"","filename":"Figure2.png","url":"https://assets-eu.researchsquare.com/files/rs-3940847/v1/f836b933a62a0abfeb67350a.png"},{"id":52106152,"identity":"01cd6fa4-6b4b-487a-92c2-6758b5a9a7da","added_by":"auto","created_at":"2024-03-06 19:36:10","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":267559,"visible":true,"origin":"","legend":"\u003cp\u003eProcess-response system for the near-surface heat transfer for bottom-heated ground at the top of the Vulcano Fossa heat pipe. (a) Morphological system: vapor ascending from the mixing zone (M\u003csub\u003edeep\u003c/sub\u003e) condenses at the 100 °C isotherm to generate heat (M\u003csub\u003econdensation\u003c/sub\u003e). Heat is transferred (t) across the two rock layers identified in Fig. 2, i.e., an unconsolidated, permeable layer (rock layer 1, t\u003csub\u003e1\u003c/sub\u003e) and a cemented surface layer (rock layer 2, t\u003csub\u003e2\u003c/sub\u003e). Heat is lost from the surface to the atmosphere (M\u003csub\u003eatmosphere\u003c/sub\u003e) by radiation (M\u003csub\u003erad\u003c/sub\u003e) and free (M\u003csub\u003efree\u003c/sub\u003e) or forced (M\u003csub\u003eforce\u003c/sub\u003e) convection. Temperature profile is from Fig. 2. (b) Cascading system for heat flow between the source (black triangle, M\u003csub\u003ein\u003c/sub\u003e) and the sink (M\u003csub\u003eout\u003c/sub\u003e), where white triangles are the heat transfer (t) mechanisms: permeable convection (t\u003csub\u003e1\u003c/sub\u003e = M\u003csub\u003econv\u003c/sub\u003e) across rock layer 1 and conduction (t\u003csub\u003e2\u003c/sub\u003e = M\u003csub\u003econd\u003c/sub\u003e) across rock layer 2. The heat source is condensation, where f\u003csub\u003eH20\u003c/sub\u003e is the water flux (kg/s), L\u003csub\u003eH20\u003c/sub\u003e is latent heat of condensation (W/kg), and A\u003csub\u003eH20\u003c/sub\u003e is the cross-sectional area of the heat pipe (m²). The heat sinks are (1) forced convection (M\u003csub\u003eforce\u003c/sub\u003e), where h\u003csub\u003ea\u003c/sub\u003e is the convective heat transfer coefficient for heat loss to the atmosphere (35 W/(m K), Matsushima et al., 2003) and T\u003csub\u003ea\u003c/sub\u003e is air temperature (K), and (2) radiation (M\u003csub\u003erad\u003c/sub\u003e), where s is the Stefan-Boltzmann constant (5.67 × 10\u003csup\u003e-8\u003c/sup\u003e W/m² K\u003csup\u003e4\u003c/sup\u003e) and e is emissivity (0.98, Maninni et al., 2018). (c) Inversion of the cascading system to obtain rock thermodynamic properties [conductivity (k), density (r) and permeability (k)] from measurements of M\u003csub\u003eout\u003c/sub\u003e, T\u003csub\u003esurf\u003c/sub\u003e and T\u003csub\u003eb\u003c/sub\u003e\u003c/p\u003e","description":"","filename":"Figure3.png","url":"https://assets-eu.researchsquare.com/files/rs-3940847/v1/94826a5b4cb2de974309fdef.png"},{"id":52106158,"identity":"89512878-e4bb-4528-8d04-6b5e2c249e31","added_by":"auto","created_at":"2024-03-06 19:36:10","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":1242317,"visible":true,"origin":"","legend":"\u003cp\u003eLocation of the 50-m long profile on the La Fossa crater. It crosses the boundary between heated and non-heated ground (dashed black line) on the eastern edge of the fumarole field.\u003c/p\u003e","description":"","filename":"Figure4.png","url":"https://assets-eu.researchsquare.com/files/rs-3940847/v1/b0654c70221c6d97ee6d6159.png"},{"id":52106150,"identity":"75dcf8d1-bde4-4717-b1cf-4cd532707eb6","added_by":"auto","created_at":"2024-03-06 19:36:09","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":817901,"visible":true,"origin":"","legend":"\u003cp\u003eT\u003csub\u003esurf\u003c/sub\u003e and T\u003csub\u003eb\u003c/sub\u003e measured on a 50-m long transect (see location on Fig. 4) across the boundary between the geothermally heated ground (hot zone) and the non-heated ground (cold zone) in a) April 2019, b) January 2020, c) October 2020, d) March 2021, e) June 2021; f) September 2021,\u003cem\u003e \u003c/em\u003eg) January 2022, h) May 2022, i) September 2022, j) March 2023, and k) June 2023\u003c/p\u003e","description":"","filename":"Figure5.png","url":"https://assets-eu.researchsquare.com/files/rs-3940847/v1/23afcb65f07b7830cca770d8.png"},{"id":52106154,"identity":"7782495c-4546-40d3-8860-fb65fd5bf579","added_by":"auto","created_at":"2024-03-06 19:36:10","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":965519,"visible":true,"origin":"","legend":"\u003cp\u003eTimes series for measured heat flux density (a) and difference in temperature between the surface and 10-cm-depth (b), and derived heat transfer coefficient (c) and soil permeability (d).\u003c/p\u003e","description":"","filename":"Figure6.png","url":"https://assets-eu.researchsquare.com/files/rs-3940847/v1/a4e3c65b2e51f5424bba4ec6.png"},{"id":52106146,"identity":"b71ee0b4-1ca9-4a39-8ff3-f011add2ea85","added_by":"auto","created_at":"2024-03-06 19:36:07","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":304839,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3940847/v1/4ee28ba2-5efb-4bc2-894b-f1577db385ad.pdf"}],"financialInterests":"","formattedTitle":"Inversion of heat loss to obtain conductivity, density and permeability at bottom-heated surfaces: The case of hydrothermal system at Vulcano between 2019 and 2023","fulltext":[{"header":"Introduction","content":"\u003cp\u003eAt vapor-dominated hydrothermal systems ascending vapor cools and boils near the surface (White et al., \u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e1971\u003c/span\u003e). In such a system, vapor ascends the geothermal \u0026ldquo;heat pipe\u0026rdquo; (White et al., \u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e1971\u003c/span\u003e) to condense at the 100\u0026deg;C isotherm (McGuiness et al., 1993). Upon condensation, liquid water descends and heat generated by condensation is transferred to the surface by permeable convection and conduction (e.g., Aubert et al., \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2008\u003c/span\u003e; Hochstein \u0026amp; Bromley, \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2005\u003c/span\u003e; Hurwitz et al., \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2012\u003c/span\u003e). Heat is then transferred from the surface to the atmosphere by radiation and free-or-forced convection (e.g., Sekioka \u0026amp; Yuhara, \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e1974\u003c/span\u003e; Matsushima et al., \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2003\u003c/span\u003e; Harris, \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2013\u003c/span\u003e). The heat transfer process from the primary source (the deep magmatic system) through the hydrothermal system to the surface is thus driven by permeable convection and conduction (Hardee, 1984). As a result rock permeability and thermal conductivity play fundamental roles in transfering heat through the system (e.g., Tanaka et al., 2017; Favorito et al., \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Stissi et al., \u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e2021\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThis is the case for the hydrothermal system beneath the Fossa crater of Vulcano (Aeolian Islands, Italy). At the Fossa, magmatic vapor ascends from a source around 2000\u0026ndash;3000 m below the crater (Ferrucci et al., \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e1991\u003c/span\u003e) to mix with meteoric and marine fluids in a biphase to vapor-monophase system (e.g., Carapezza et al., \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e1981\u003c/span\u003e; Chiodini \u0026amp; Cioni, 1995; Nuccio et al. \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e1999\u003c/span\u003e) at a depth of 500\u0026ndash;1500 m (Alparone et al., \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2010\u003c/span\u003e). Efficiency of heat flow up the \u0026ldquo;heat pipe\u0026rdquo; above the mixing zone is strongly dependent on permeability (Diliberto, \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2011\u003c/span\u003e, \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2017\u003c/span\u003e; Harris et al., \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2012\u003c/span\u003e), especially over the last few hundred meters of ascent (Nuccio et al., \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e1999\u003c/span\u003e). Water condensing near-surface at the 100\u0026deg;C isotherm generates heat that creates a surface thermal anomaly at the head of the heat pipe (Chiodini et al., \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2005\u003c/span\u003e; Aubert et al., 2019). The heat pipe is tightly culminated by self-sealing, creating a high permeability zone where mass and heat fluxes are concentrated (Harris \u0026amp; Maciejewski, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2000\u003c/span\u003e; Chiodini et al., \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2005\u003c/span\u003e; Mannini et al., \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2019\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eIn April 2019 we set up an experiment in the Vulcano Fossa crater that allowed us to measure the surface and soil temperatures at the head of the heat pipe, simultaneous with heat flux derived from ASTER (Advanced Spaceborne Thermal Emission and Reflection Radiometer). This allows us to assess the morphological and thermal conditions of the thermal boundary layer between the heat source (condensation) and sink (surface heat losses) and construct an open, cascading system for heat transfer from the source to the sink. Inversion of the model allows the rock thermodynamic properties (conductivity, density and permeability) to be quantified. Given continuity in these measurements through 2023 (Pailot-Bonn\u0026eacute;tat \u0026amp; Harris, 2023) allows us to track changes in permeability before, during and after the period of unrest that began in 2021.\u003c/p\u003e"},{"header":"Models and Methods","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003eHeat transfer model\u003c/h2\u003e \u003cp\u003eFollowing McGuiness et al. (1993), we set up a heat transfer model whereby ascending vapor arriving at the 100°C isotherm condenses to generate heat. Heat generated by condensation is then transferred to the surface by permeable convection and conduction (Hochstein \u0026amp; Bromley, \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2005\u003c/span\u003e; Hurwitz et al., \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2012\u003c/span\u003e). This sets up a thermal gradient that declines over a typical height of 1–10 m from 100°C to ≤ 30–50°C near the surface (e.g., Dobson et al., \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2003\u003c/span\u003e; Chiodini et al., \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2005\u003c/span\u003e; Aubert et al., 2018).\u003c/p\u003e \u003cp\u003eWe adapt this model to the near-surface morphology of the Vulcano Fossa, as defined from a trench dug in June 2021. This revealed that the thermal gradient at the Fossa crosses two main rock layers: a lower zone of altered breccia and a cemented surface layer (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). The immediate sub-surface (rock layer 1, Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e) is unconsolidated and comprises altered cm-blocks of trachyte in a sand-ash matrix (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). Below 60 cm mineralization is apparent, and blocks are altered to clay. Discontinuous layers of thin, hard, cemented duripan can also be found below 70 cm (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). The surface layer is a 5-to-10 cm-thick case-hardened crust of cemented silt, sand and trachytic blocks (rock layer 2, Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). Case hardened crusts are “hard, resilient crusts on the surfaces of boulders and outcrops of soft, porous rock caused through the filling of voids with natural cement” (Goudie, \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2000\u003c/span\u003e; Viles and Goudie, \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2004\u003c/span\u003e). Such crusts have been described on the Keanakakoi deposits of Kilauea, where they result from cementing of the silt-sand matrix due to silicate and sulfate mineral deposition from passage of acid gasses and fluids (Malin et al., \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e1983\u003c/span\u003e); as is the case at Vulcano. Such cemented layers self-seal the system, where particle agglutination and pore filling with minerals reduces air and water circulation (Rammlmair, \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2002\u003c/span\u003e). Such cemented layers are associated with high thermal conductivities (Piqueux \u0026amp; Christensen, \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2009\u003c/span\u003e). Thus, following Hardee (1984) and Aubert et al. (1998), our model considers heat transfer (τ) across the upper cemented layer (rock layer 2) to be dominated by conduction, with τ across lower unconsolidated layer (rock layer 1) being dominated by permeable convection (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ea).\u003c/p\u003e \u003cp\u003eThe profile of air temperature in the first meter above the surface reveals a thermal boundary layer of height 40 cm (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). Across the boundary layer, air temperature decreases from 34.5 to 32.5°C, i.e., 0.5°C per meter, to stabilize at between 32 and 32.5°C. Following Incropora et al. (\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2017\u003c/span\u003e), velocity of the fluid at the base of the boundary layer will be zero and air temperature will equal surface temperature. Below the surface, the temperature profile has the form T = -49.7y² + 113.6y + 35 (R² = 0.9997) (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e), which projects the 100°C isotherm to be at a depth of 1.05 ± 0.05 m.\u003c/p\u003e \u003cp\u003eBased on this morphological system, we build a cascading system where heat transfer from the source (M\u003csub\u003ein\u003c/sub\u003e, condensation of ascending vapor) to the sink (M\u003csub\u003eout\u003c/sub\u003e, radiation and convection to the atmosphere) is described by permeable convection across rock layer 1 of height H. Instead, heat transfer across rock layer 2, of height h, is by conduction (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eb).\u003c/p\u003e \u003cp\u003eFollowing Hardee (1984), permeable convection (M\u003csub\u003econv\u003c/sub\u003e in W m\u003csup\u003e-2\u003c/sup\u003e) can be described by:\u003c/p\u003e \u003cp\u003e \u003c/p\u003e\u003cdiv class=\"gridtable\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003ctable float=\"No\" id=\"Taba\" border=\"1\"\u003e\u003ccolgroup cols=\"2\"\u003e\u003c/colgroup\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eM\u003csub\u003econv\u003c/sub\u003e = h\u003csub\u003ec\u003c/sub\u003e (T\u003csub\u003e100\u003c/sub\u003e-T\u003csub\u003eb\u003c/sub\u003e)\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e(1)\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/table\u003e\u003c/div\u003e \u003cp\u003e\u003c/p\u003e\u003cp\u003ein which T\u003csub\u003e100\u003c/sub\u003e is boiling temperature, T\u003csub\u003eb\u003c/sub\u003e is the temperature at the interface of rock layers 1 and 2, and h\u003csub\u003ec\u003c/sub\u003e is the convective heat transfer coefficient (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eb). Following Holman (1994), the convective heat transfer coefficient can be related to the Nusselt Number (Nu) in:\u003c/p\u003e \u003cp\u003e \u003c/p\u003e\u003cdiv class=\"gridtable\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003ctable float=\"No\" id=\"Tabb\" border=\"1\"\u003e\u003ccolgroup cols=\"2\"\u003e\u003c/colgroup\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eh\u003csub\u003ec\u003c/sub\u003e = (k Nu / H)\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e(2)\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/table\u003e\u003c/div\u003e \u003cp\u003e\u003c/p\u003e \u003cp\u003ewhere k is rock thermal conductivity. For a bottom heated surface with a colder top surface (Incropera et al., 2017),\u003c/p\u003e \u003cp\u003e \u003c/p\u003e\u003cdiv class=\"gridtable\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003ctable float=\"No\" id=\"Tabc\" border=\"1\"\u003e\u003ccolgroup cols=\"2\"\u003e\u003c/colgroup\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNu = 0.54 Ra\u003csup\u003e1/4\u003c/sup\u003e(10\u003csup\u003e4\u003c/sup\u003e ≲ Ra ≲ 10\u003csup\u003e7\u003c/sup\u003e)\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e(3a)\u003c/p\u003e \u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNu = 0.15 Ra\u003csup\u003e1/3\u003c/sup\u003e(10\u003csup\u003e7\u003c/sup\u003e ≲ Ra ≲ 10\u003csup\u003e11\u003c/sup\u003e)\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e(3b)\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/table\u003e\u003c/div\u003e \u003cp\u003e\u003c/p\u003e\u003cp\u003eRa being the Rayleigh Number, written in terms of permeability (κ) is (cf. Wicky \u0026amp; Hauck, \u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e2020\u003c/span\u003e):\u003c/p\u003e\u003cp\u003e \u003c/p\u003e\u003cdiv class=\"gridtable\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003ctable float=\"No\" id=\"Tabd\" border=\"1\"\u003e\u003ccolgroup cols=\"2\"\u003e\u003c/colgroup\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRa = [ρ² c\u003csub\u003ea\u003c/sub\u003e g β H (T\u003csub\u003e100\u003c/sub\u003e - T\u003csub\u003eb\u003c/sub\u003e) κ] / [µ k]\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e(4)\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/table\u003e\u003c/div\u003e \u003cp\u003e\u003c/p\u003e \u003cp\u003eHere, g is acceleration due to gravity, ρ is the density of the rock, c\u003csub\u003ea\u003c/sub\u003e and µ are the specific heat capacity and dynamic viscosity of steam, and β is the coefficient of thermal expansion [i.e., 1/T, with T being (T\u003csub\u003e100\u003c/sub\u003e + T\u003csub\u003eb\u003c/sub\u003e)/2].\u003c/p\u003e \u003cp\u003eIn its most simple form, conduction (M\u003csub\u003econd\u003c/sub\u003e in W m\u003csup\u003e-2\u003c/sup\u003e) can be described using Fourier’s Law:\u003c/p\u003e \u003cp\u003e \u003c/p\u003e\u003cdiv class=\"gridtable\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003ctable float=\"No\" id=\"Tabe\" border=\"1\"\u003e\u003ccolgroup cols=\"2\"\u003e\u003c/colgroup\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eM\u003csub\u003econd\u003c/sub\u003e = k (ΔT/h)\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e(5)\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/table\u003e\u003c/div\u003e \u003cp\u003e\u003c/p\u003e\u003cp\u003ein which ΔT is T\u003csub\u003eb\u003c/sub\u003e-T\u003csub\u003esurf\u003c/sub\u003e, T\u003csub\u003esurf\u003c/sub\u003e being the surface temperature (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eb). In Eq.\u0026nbsp;(5), conductivity can be related to rock density using thermal diffusivity (α) and specific heat capacity (c\u003csub\u003ep\u003c/sub\u003e) through:\u003c/p\u003e \u003cp\u003e \u003c/p\u003e\u003cdiv class=\"gridtable\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003ctable float=\"No\" id=\"Tabf\" border=\"1\"\u003e\u003ccolgroup cols=\"2\"\u003e\u003c/colgroup\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eα = k / (ρ c\u003csub\u003ep\u003c/sub\u003e)\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e(6)\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/table\u003e\u003c/div\u003e \u003cp\u003e\u003c/p\u003e \u003cp\u003eWe assume that all heat convected across rock layer 1 is conducted through rock layer 2 to be lost from the surface (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ea), so that M\u003csub\u003ein\u003c/sub\u003e = M\u003csub\u003econv\u003c/sub\u003e ≈ M\u003csub\u003econd\u003c/sub\u003e = M\u003csub\u003eout\u003c/sub\u003e. Now, given a measurement of the surface leaving heat flux (M\u003csub\u003eout\u003c/sub\u003e), temperatures T\u003csub\u003esurf\u003c/sub\u003e, T\u003csub\u003eb\u003c/sub\u003e and T\u003csub\u003e100\u003c/sub\u003e, and the thermodynamic properties of steam, the system can be inverted to solve for the three key thermodynamic properties of the rock: conductivity, density of layer 2 and permeability of layer 1 (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ec). Thus, to solve for k, ρ and κ, we thus measure M\u003csub\u003eout\u003c/sub\u003e, T\u003csub\u003esurf\u003c/sub\u003e and T\u003csub\u003eb\u003c/sub\u003e (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eb), and use c\u003csub\u003ea\u003c/sub\u003e of 4190 J/(kg K) and 3.77 × 10\u003csup\u003e− 4\u003c/sup\u003e Pa s for µ (for steam at 75°C, \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://www.ski-gmbh.com/swa/tools/steam\u003c/span\u003e\u003cspan address=\"https://www.ski-gmbh.com/swa/tools/steam\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003eInput measurements\u003c/h2\u003e \u003cp\u003eHeat loss data from the surface to the atmosphere (M\u003csub\u003eout\u003c/sub\u003e = M\u003csub\u003eatmosphere\u003c/sub\u003e, Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e) were obtained from thermal infrared images (10.95–11.65 µm, 90 × 90 pixel) acquired by ASTER. The surface temperatures are taken from the AST_08 products in which emissivity corrections and atmospheric corrections have already been performed automatically. Heat is lost by radiation (M\u003csub\u003erad\u003c/sub\u003e) and forced convection (M\u003csub\u003econv\u003c/sub\u003e) which can be described by Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e:\u003c/p\u003e \u003cp\u003e \u003c/p\u003e\u003cdiv class=\"gridtable\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003ctable float=\"No\" id=\"Tabg\" border=\"1\"\u003e\u003ccolgroup cols=\"2\"\u003e\u003c/colgroup\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eM\u003csub\u003eforce\u003c/sub\u003e = h\u003csub\u003ea\u003c/sub\u003e (T\u003csub\u003emax\u003c/sub\u003e-T\u003csub\u003eambient\u003c/sub\u003e)\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e(7)\u003c/p\u003e \u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eM\u003csub\u003erad\u003c/sub\u003e = σ ε (T\u003csub\u003emax\u003c/sub\u003e\u003csup\u003e4\u003c/sup\u003e-T\u003csub\u003eambient\u003c/sub\u003e\u003csup\u003e4\u003c/sup\u003e)\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e(8)\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/table\u003e\u003c/div\u003e \u003cp\u003e\u003c/p\u003e \u003cp\u003ein which T\u003csub\u003emax\u003c/sub\u003e is the maximum temperature of the thermally anomalous pixels in La Fossa crater, T\u003csub\u003eambient\u003c/sub\u003e is the average temperature of the inactive Vulcanello cone at the northern end of Vulcano, h\u003csub\u003ea\u003c/sub\u003e is the atmospheric convective heat transfer coefficient (35 W m\u003csup\u003e-2\u003c/sup\u003e K\u003csup\u003e-1\u003c/sup\u003e following Matsushima et al. (\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2003\u003c/span\u003e), σ is the Stefan-Boltzmann constant, and ε is the emissivity of the ground surface (0.98).\u003c/p\u003e \u003cp\u003eOn 29 April 2019 at 22h30 (CET), three thermally anomalous pixels were found over the Fossa. The atmospherically corrected temperatures (T\u003csub\u003esurf\u003c/sub\u003e = 17.9, 18.4 and 16.7°C) were converted to radiative and convective heat losses (M\u003csub\u003erad\u003c/sub\u003e and M\u003csub\u003eforce\u003c/sub\u003e) using ambient temperatures (T\u003csub\u003ea\u003c/sub\u003e) of 11.2, 11.4 and 12.6°C (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eb) following the approach of Mannini et al. (\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). This gave M\u003csub\u003erad\u003c/sub\u003e of 30 ± 10 W/m² and M\u003csub\u003eforce\u003c/sub\u003e of 210 ± 60 W/m², for a total heat loss from the bottom heated surface (M\u003csub\u003eout\u003c/sub\u003e, Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ea) of 240 ± 70 W/m². A total of 11 field campaigns were made following the April 2019 experiment with 30 near-simultaneous ASTER overpasses. The data for each overpass, and calculated M\u003csub\u003eout\u003c/sub\u003e are given in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. We used the data from the closest overpass in time to our field campaigns as input in the inversion model.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e\u003cdiv class=\"gridtable\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eList of available ASTER night-time overpasses close in time to our field campaigns with T\u003csub\u003emax\u003c/sub\u003e and T\u003csub\u003eambient\u003c/sub\u003e used to calculate M\u003csub\u003erad\u003c/sub\u003e, M\u003csub\u003eforce\u003c/sub\u003e and M\u003csub\u003eout\u003c/sub\u003e (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e).\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e\u003ccolgroup cols=\"6\"\u003e\u003c/colgroup\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDate\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eT\u003csub\u003emax\u003c/sub\u003e (°C)\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eT\u003csub\u003eambient\u003c/sub\u003e (°C)\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eM\u003csub\u003eforce\u003c/sub\u003e (W/m²)\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eM\u003csub\u003erad\u003c/sub\u003e (W/m²)\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eM\u003csub\u003eout\u003c/sub\u003e (W/m²)\u003c/p\u003e \u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e04/29/19\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e18.4\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e11.4\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e210\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e240\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e01/30/20\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e18.6\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e9.9\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e303\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e46\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e349\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e10/28/20\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e20.6\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e12.6\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e279\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e43\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e322\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e02/17/21\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e17.4\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e10.9\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e225\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e34\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e259\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e03/12/21\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e19.3\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e11.2\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e282\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e43\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e325\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e04/06/21\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e18.3\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e15.5\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e96\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e15\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e110\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e04/13/21\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e19.1\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e13.0\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e211\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e32\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e243\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e05/08/21\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e24.1\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e17.2\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e241\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e39\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e280\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e05/24/21\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e24.4\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e19.8\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e159\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e26\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e184\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e05/31/21\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e24.6\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e19.8\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e166\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e27\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e193\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e06/25/21\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e35.8\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e26.9\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e312\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e56\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e367\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e07/11/21\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e32.6\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e27.4\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e182\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e32\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e214\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e07/18/21\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e30.8\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e24.2\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e231\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e40\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e270\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e07/27/21\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e34.1\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e26.9\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e251\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e45\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e296\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e08/12/21\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e35.8\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e27.9\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e276\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e50\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e326\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e08/19/21\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e37.4\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e27.7\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e339\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e61\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e400\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e08/28/21\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e33.4\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e26.9\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e225\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e40\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e265\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e09/13/21\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e32.7\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e23.4\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e323\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e56\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e379\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e09/20/21\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e32.3\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e22.7\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e333\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e58\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e391\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e09/29/21\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e32.0\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e22.9\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e318\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e55\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e373\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e12/01/21\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e26.7\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e15.2\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e400\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e65\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e465\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e01/19/22\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e23.0\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e9.3\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e478\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e73\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e551\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e01/26/22\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e18.7\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e6.7\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e418\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e62\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e480\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e02/04/22\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e24.8\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e11.6\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e461\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e72\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e534\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e03/08/22\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e18.0\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e7.7\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e359\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e53\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e412\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e03/15/22\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e21.1\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e10.7\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e364\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e56\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e420\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e03/24/22\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e23.4\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e10.4\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e453\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e70\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e523\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e09/07/22\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e34.9\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e23.7\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e390\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e68\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e458\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e01/12/23\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e20.8\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e12.6\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e286\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e44\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e331\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e06/26/23\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e30.7\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e25.4\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e182\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e32\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e214\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/table\u003e\u003c/div\u003e \u003cp\u003e\u003c/p\u003e \u003cp\u003eTo provide data for T\u003csub\u003esurf\u003c/sub\u003e and T\u003csub\u003eb\u003c/sub\u003e we completed temperature measurements of the suface with a thermal infrared thermometer and obtained temperature at a depth of 10 cm using a k-type thermocouple inserted into holes drilled through the surface layer (rock layer 2, Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). Measurements were made every 5 m along a 50 m transect that traversed the eastern edge of the hydrothermally heated area (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e). On the day of the ASTER acquisition, 29 April 2019, this gives a T\u003csub\u003esurf\u003c/sub\u003e of 31 ± 5°C and T\u003csub\u003eb\u003c/sub\u003e of 30 ± 4°C for the non-heated zone, so that ΔT ≈ 0. However, in the thermal zone we have T\u003csub\u003esurf\u003c/sub\u003e of 37 ± 4°C and T\u003csub\u003eb\u003c/sub\u003e of 55 ± 10°C, so that ΔT = 18 ± 6°C. All temperature profiles of T\u003csub\u003esurf\u003c/sub\u003e and T\u003csub\u003eb\u003c/sub\u003e collected between 2019 and 2024 are given in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e, and temperature data are summaried in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e\u003cdiv class=\"gridtable\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eMean T\u003csub\u003esurf\u003c/sub\u003e and T\u003csub\u003eb\u003c/sub\u003e (with standard deviation as error) collected during the field campaigns of 2019–2023 for the cold and hot zones along the 50 m transect (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e).\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e\u003ccolgroup cols=\"9\"\u003e\u003c/colgroup\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e\u003cth align=\"left\" colspan=\"4\" nameend=\"c5\" style=\"background: rgb(231, 230, 230);\" namest=\"c2\"\u003e \u003cp\u003eCOLD ZONE\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colspan=\"4\" nameend=\"c9\" namest=\"c6\" style=\"background: rgb(251, 228, 213);\"\u003e \u003cp\u003eHOT ZONE\u003c/p\u003e \u003c/th\u003e\u003c/tr\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDate\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eT\u003csub\u003esurf\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e±σ\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eT\u003csub\u003eb\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e±σ\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eT\u003csub\u003esurf\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003e±σ\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003eT\u003csub\u003eb\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e\u003cth align=\"left\" colname=\"c9\"\u003e \u003cp\u003e±σ\u003c/p\u003e \u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e04/29/19\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e31\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e37\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e55\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e01/31/20\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e26\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e24\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e30\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e63\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e17\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e10/19/20\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e25\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e24\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e32\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e48\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e14\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e03/19/21\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e18\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e15\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e46\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e19\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e06/14/21\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e38\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e35\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e34\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e7\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e60\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e14\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e09/18/21\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e45\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e49\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e21\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e51\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e81\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e11\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e01/12/22\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e15\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e29\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e14\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e26\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e65\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e19\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e05/29/22\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e31\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e38\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e7\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e36\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e67\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e15\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e09/07/22\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e44\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e40\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e54\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e66\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e14\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e03/13/23\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e31\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e28\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e39\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e54\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e18\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e06/26/23\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e31\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e36\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e37\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e57\u003c/p\u003e \u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e15\u003c/p\u003e \u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/table\u003e\u003c/div\u003e \u003cp\u003e\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e "},{"header":"Results: Inversion of the heat transfer model","content":"\u003ch2\u003eThermal conductivity and density, April 2019\u003c/h2\u003e\u003cp\u003eUsing the value of M\u003csub\u003eout\u003c/sub\u003e (240 ± 70 W/m²) for M\u003csub\u003econd\u003c/sub\u003e in Eq.\u0026nbsp;(5), with the ΔT of 18 ± 6°C (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e) and h of 7.5 ± 2.5 cm, as measured on April 29, 2019, we obtain a thermal conductivity of 1.0 ± 0.3 W/(m K). This compares with a thermal conductivity of 0.8 ± 0.25 W/(m K) calculated for Vulcano by Aubert et al. (\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2008\u003c/span\u003e). To obtain density of layer 2 (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e), we thus use a thermal conductivity of 1.0 ± 0.3 W/(m K) and rearrange Eq.\u0026nbsp;(6). To solve, we use a rock thermal diffusivity of 0.4 ± 0.13 × 10\u003csup\u003e− 6\u003c/sup\u003e m²/s, these being the values found for thermal ground at New Zealand’s Wairakei hydrothermal system by Hochstein and Bromley (\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2005\u003c/span\u003e), and 1025 ± 25 J/(kg K) for the specific heat capacity [after Hardee (1982) and Stissi et al. (\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e2021\u003c/span\u003e)]. This gives a density of 2440 ± 120 kg/m\u003csup\u003e3\u003c/sup\u003e for rock layer 2, which compares with a dense rock density for trachyte of 2700 kg/m\u003csup\u003e3\u003c/sup\u003e (Prival et al., \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e2022\u003c/span\u003e) and a bulk density for debris flows at Vulcano comprising the same components as rock layer 2 of 1950 kg/m\u003csup\u003e3\u003c/sup\u003e (Ferrucci et al., \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2005\u003c/span\u003e).\u003c/p\u003e\u003ch2\u003ePermeabillity, April 2019\u003c/h2\u003e\u003cp\u003eThe measurements along the transect on April 29, 2019 gave T\u003csub\u003eb\u003c/sub\u003e of 55 ± 10°C (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e), and measurements in the trench show that the depth to the 100°C isotherm (H) was 1.0 ± 0.1 m (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). Using these values with M\u003csub\u003econv\u003c/sub\u003e of 240 ± 70 W/m² and thermal conductivity of 1.0 ± 0.3 W/(m K) in rearranged forms of Equations (1), (2) and (3) gives a convective heat transfer coefficient of 5.3 ± 2.2 W/(m² K), and a Nusselt number of 5 ± 1 and Rayleigh number of 9.5 ± 6.7 × 10\u003csup\u003e3\u003c/sup\u003e. Now, using these values in a re-arranged form of Eq.\u0026nbsp;(4), with a density of 2440 ± 120 kg/m\u003csup\u003e3\u003c/sup\u003e, we obtain a permeability for layer 1 (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e) of between 1.1 × 10\u003csup\u003e–10\u003c/sup\u003e and 1.9 × 10\u003csup\u003e–11\u003c/sup\u003e m². This permeability range spans that used by Tanaka et al. (2017), i.e., 5.0 × 10\u003csup\u003e–10\u003c/sup\u003e m², to numerically model heat flux in the “conduit” zone feeding the hydrothermal system of Mt. Tokachidake (Japan). However, our premeability is a little higher than those derived from numerical simulations of heat and mass transfer at Vulcano by Stissi et al. (\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e2021\u003c/span\u003e), i.e., 1.25–8.2 × 10\u003csup\u003e–12\u003c/sup\u003e m². This is no doubt due to the model of Stissi et al. (\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e2021\u003c/span\u003e) considering depths down to -1500 m, whereas our model is for the final meter of heat transfer. At depth, argillic alteration and sealing will serve to decrease permeability (Dobson et al., \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2003\u003c/span\u003e; Julia et al., \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2014\u003c/span\u003e), so that the median permeability for the heat pipe above the mixing zone at Vulcano is likely of the order of 10\u003csup\u003e–11\u003c/sup\u003e m², being 10\u003csup\u003e–12\u003c/sup\u003e m² at depth and 10\u003csup\u003e–10\u003c/sup\u003e m² near-surface.\u003c/p\u003e"},{"header":"Discussion: Permeability evolution at Vulcano, 2019–2023","content":"\u003cp\u003eVulcano entered a new phase of unrest in 2021, which culiminated in an increase in T\u003csub\u003eb\u003c/sub\u003e at our control site from 25°C on September 11 to 69°C by October 7 (Pailot-Bonnétat \u0026amp; Harris, \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). This was coupled with an increase in the area of the thermal anomaly recorded in ASTER data from 7 to 35 pixels. As a result, the total heat flux increased from baseline levels of ~ 40 MW in March 2021 to a peak of 120 MW in March 2022 (Pailot-Bonnétat et al., \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2023\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eOur ASTER-derived heat fluxes between April 2019 and June 2023, and spanning the unrest, are given in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003ea and field-measured ΔT in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003eb, with derived heat transfer coefficient and permeability in Figs.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003ec and \u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003ed. We see an increase in heat flux from 350 W/m² in 2021 to almost 550 W/m² by the middle of 2022 (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003ea), with ΔT peaking at the same time (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003eb). In parallel with this, the efficiency of heat transfer, as described by h\u003csub\u003ec\u003c/sub\u003e, increased from a relatively stable level of ~ 5 W/(m² K) from 2019 through the first half of 2021, to ~ 20 W/(m² K) by September 2021 (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003ec). This was matched by a peak in permeability at around 10\u003csup\u003e− 7\u003c/sup\u003e m², compared with 2019–2021 levels of 10\u003csup\u003e− 9\u003c/sup\u003e to 10\u003csup\u003e–10\u003c/sup\u003e (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003ed). All parameters began to decline during 2022 to reach pre-unrest levels by 2023 (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eAuippa et al. (2022) ascribes the onset of unrest to the presence of ~ 3 × 10\u003csup\u003e6\u003c/sup\u003e m\u003csup\u003e3\u003c/sup\u003e mafic magma at a depth of 4–5 km, with this magma probably being injected around the beginning of 2021 when the first signs of unrest were recorded (Pailot-Bonnétat et al., \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). Sealed-zones failed in September 2021, when a widespread increase in permeability caused expansion in the area of soil degassing (Federico et al., \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Pailot-Bonnétat et al., \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). At this point we record an increase in permeability of the upper portion of the heat pipe, which increased the efficiency of the heat transfer process (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e). By the second half of 2022 our two main metrics of unrest, M\u003csub\u003eout\u003c/sub\u003e (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003ea) and ΔT (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003eb), were turning around. Application of our heat transfer model suggests that this was associated with re-sealing to bring permeabilities (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003ed), and hence the heat transfer coefficient (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003ec), back to the pre-unrest levels.\u003c/p\u003e"},{"header":"Conclusions","content":"\u003cp\u003eWe show here how simple field-based temperature measurements, coupled with derivation of heat flux density from near-simultaneous overpasses of satellites carrying infrared sensors, can be used to derive and track permeability. For near-surface heat transfer at hydrothermal system, permeability is the main driver controlling heat fluxes across a heat pipe extending between a fluid mixing zone and the surface. To derive and track permeability, we need to build a Rayleigh-number driven heat transfer model for a bottom-heated surface. At Vulcano, we find that the model allows us to track changes in permeability that drive variations in heat flux density and soil temperatures during transition from baseline to unrest levels, and back again. While the order of magnitude of permeabilities obtained here can be used for modelling (e.g., Tanaka et al., 2017; Favorito et al., \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Stissi et al., \u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e2021\u003c/span\u003e), the methodology can be used to assess permeabilities at other hydrothermal systems, and the heat transfer model can be used as a basis to fully constrain heat flux from source to sink at a hydrothermal system.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003eAcknowledgments\u003c/p\u003e\n\u003cp\u003eWe thank Mike Ramsey (University of Pittsburgh) for help with triggering the ASTER Urgent Response Protocol for timely image provision. Guillaume Boudoire, Roxane Buso, Iole Serena Diliberto, Alessando Gattuso, Fausto Grassa, Nicolas Levillayer, Stefano Mannini, Victoria Rafflin, Luca Teray, and Benjamin Van Wyk de Vries are thanked for field implementation and science discussions. We are most grateful to INGV-Palermo for making the facilities at the Carapezza Center on the island of Vulcano open and available to us. Finally, working through the Covid-19 global pandemic would not have been possible without the help and support of Tanino at the Casa Genovese (Vulcano), Maurizio at \u0026quot;La Forgia\u0026quot; (Vulcano), Manfreddi at La Giarra (Vulcano), all at the Filadelfia (Lipari), the \u0026ldquo;Faraglione\u0026rdquo; bar, and the Carabinieri of both Vulcano and Lipari.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis work was financed by the Agence National de la Recherche (ANR) through the project DIRE (Program: CES 04 Innovations scientifques et technologiques pour accompagner la transition \u0026eacute;cologique: project no.: ANR-19-CE04-0014\u0026ndash;01) and Labex Clervolc project no. 2019\u0026ndash;22. This is contribution no. XXX of the ClerVolc program of the International Research Center for Disaster Sciences and Sustainable Development of the University of Clermont Auvergne.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConflicts of interest/Competing interests\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNot applicable\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAvailability of data and material\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eAll data sets are freely available as Supplementary Information, as part of a spreadsheet in which the model is also set-up. The data and model can be used with DOI reference to this paper and the acknowledgment \u0026ldquo;Data provided by Laboratoire Magmas et Volcans, Universit\u0026eacute; Clermont Auvergne, Aubi\u0026egrave;re, France from the ANR-DIRE network as part of project Data-Integration, Risk and the Environment\u0026rdquo;.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCode availability\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNot applicable\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eAiuppa, A., Bitetto, M., Calabrese, S., Delle Donne, D., Lages, J., La Monica, F. P., et al. (2022). Mafic magma feeds degassing unrest at Vulcano Island, Italy. \u003cem\u003eCommunications Earth and Environment\u003c/em\u003e, \u003cem\u003e3\u003c/em\u003e(1). https://doi.org/10.1038/s43247-022-00589-1\u003c/li\u003e\n\u003cli\u003eAlparone, S., Cannata, A., Gambino, S., Gresta, S., Milluzzo, V., \u0026amp; Montalto, P. (2010). 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Air Convection in the Active Layer of Rock Glaciers. \u003cem\u003eFrontiers in Earth Science\u003c/em\u003e, \u003cem\u003e8\u003c/em\u003e. https://doi.org/10.3389/feart.2020.00335\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"bulletin-of-volcanology","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"buvo","sideBox":"Learn more about [Bulletin of Volcanology](http://link.springer.com/journal/445)","snPcode":"445","submissionUrl":"https://www.editorialmanager.com/buvo/default2.aspx","title":"Bulletin of Volcanology","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Heat flux, Hydrothermal system, permeability, conductivity, Vulcano, ASTER","lastPublishedDoi":"10.21203/rs.3.rs-3940847/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3940847/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eAt hydrothermal systems, heat transfer across the final surface layer is driven by permeable convection and conduction, so that permeability and conductivity play fundamental roles in controlling the 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/m\u0026sup2;), surface temperature, and soil temperature to solve for soil conductivity, density, and permeability. At Vulcano in 2019, we measured an ASTER-derived heat flux density of 240\u0026thinsp;\u0026plusmn;\u0026thinsp;70 W/m\u0026sup2;, and a difference between soil and surface temperature of 18\u0026thinsp;\u0026plusmn;\u0026thinsp;6\u0026deg;C. The surface layer is a 7.5\u0026thinsp;\u0026plusmn;\u0026thinsp;2.5 cm thick case hardened crust across which heat transfer is conduction dominated. We invert our heat transfer model by using the derived temperature (T) gradient of T = -49.7y\u0026sup2; + 113.6y\u0026thinsp;+\u0026thinsp;35 (R\u0026sup2; = 0.9997), where y is depth in meters between the surface and 70 cm. The result is a conductivity for the case hardened layer of 1.0\u0026thinsp;\u0026plusmn;\u0026thinsp;0.3 W/(m K) and density of 2440\u0026thinsp;\u0026plusmn;\u0026thinsp;120 kg/m\u003csup\u003e3\u003c/sup\u003e. Below the case harded layer heat transfer is dominated by permeable convection, and a soil comprised of highly altered trachytic blocks in an ash matrix. Our model gives permeabilities of 1\u0026ndash;19 \u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;10\u003c/sup\u003e m\u0026sup2; of 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\u003csup\u003e\u0026minus;\u0026thinsp;7\u003c/sup\u003e m\u0026sup2;. 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.\u003c/p\u003e","manuscriptTitle":"Inversion of heat loss to obtain conductivity, density and permeability at bottom-heated surfaces: The case of hydrothermal system at Vulcano between 2019 and 2023","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-03-06 19:36:00","doi":"10.21203/rs.3.rs-3940847/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Moderate revision (possibly re-reviewed)","date":"2024-04-03T04:35:24+00:00","index":"","fulltext":""},{"type":"reviewerAgreed","content":"","date":"2024-03-03T20:44:54+00:00","index":0,"fulltext":""},{"type":"editorAssigned","content":"","date":"2024-02-22T07:09:13+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"Bulletin of Volcanology","date":"2024-02-20T07:38:07+00:00","index":"","fulltext":""},{"type":"submitted","content":"Bulletin of Volcanology","date":"2024-02-07T09:10:12+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"bulletin-of-volcanology","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"buvo","sideBox":"Learn more about [Bulletin of Volcanology](http://link.springer.com/journal/445)","snPcode":"445","submissionUrl":"https://www.editorialmanager.com/buvo/default2.aspx","title":"Bulletin of Volcanology","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"f4f81bd0-748d-4563-8900-1983b57eb0bf","owner":[],"postedDate":"March 6th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2024-06-11T09:07:55+00:00","versionOfRecord":{"articleIdentity":"rs-3940847","link":"https://doi.org/10.1007/s00445-024-01746-4","journal":{"identity":"bulletin-of-volcanology","isVorOnly":false,"title":"Bulletin of Volcanology"},"publishedOn":"2024-05-20 09:07:55","publishedOnDateReadable":"May 20th, 2024"},"versionCreatedAt":"2024-03-06 19:36:00","video":"","vorDoi":"10.1007/s00445-024-01746-4","vorDoiUrl":"https://doi.org/10.1007/s00445-024-01746-4","workflowStages":[]},"version":"v1","identity":"rs-3940847","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-3940847","identity":"rs-3940847","version":["v1"]},"buildId":"WrCJVZZCHTDjtuVLN7oU0","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}