Thermal diffusivity of seasonal snow determined from temperature profiles

Thermal diffusivity of snow is an important thermodynamic property associated with key hydrological phenomena such as snow melt and heat and water vapor exchange with the atmosphere. Direct determination of snow thermal diffusivity requires coupled point measurements of thermal conductivity and density, which continually change due to snow metamorphism. Traditional methods for determining these two quantities are generally limited by temporal resolution. In this study we present a method to determine the thermal diffusivity of snow with high temporal resolution using snow temperature profile measurements. High resolution (between 2.5 and 10 cm at 1 min) temperature measurements from the seasonal snow pack at the Plaine-Morte glacier in Switzerland are used as initial conditions and Neumann (heat flux) boundary conditions to numerically solve the one-dimensional heat equation and iteratively optimize for thermal diffusivity. The implementation of Neumann boundary conditions and a t-test, ensuring statistical significance between solutions of varied thermal diffusivity, are important to help constrain thermal diffusivity such that spurious high and low values as seen with Dirichlet (temperature) boundary conditions are reduced. The results show that time resolved thermal diffusivity can be determined from temperature measurements of seasonal snow and support density-based empirical parameterizations for thermal conductivity.     

Determination of upward/downward groundwater fluxes using transient variations of soil profile temperature: test of the method with Voyons (Aube,France) experimental data

The temperature variations recorded at several points of a vertical shallow‐depth profile are governed both by conductive and convective heat transfers and can be used to calculate the vertical component of the Darcy velocity and thermal diffusivity in the soil. This paper describes such calculations when transient variations over tens of days are considered and tests them using data collected at Voyons (Aube, France). The temperature was recorded during a year and a half period with a 1 h sampling time step at three different depths: 0·2, 0·4 and 0·75 m. By processing the annual variation of temperature, we obtained a value of the Darcy velocity in good agreement with the value of actual/potential evapotranspiration ratio. By processing transient variations, despite the limitation of the calculations due to the lack of sensitivity of the sensors, results obtained at Voyons were in good correlation with tensiometric data. Copyright © 2005 John Wiley & Sons, Ltd.     

The thermal structure of a shallow lake in early winter

The thermal structure of a shallow lake in the first month of its freeze up is shown to vary widely from year to year. The rate of temperature increase at different horizons of the water mass in early winter is evaluated, and warming of shallow and deep-water areas in the lake are shown to be uneven. The distribution of near-bed temperature as a function of water depth in the first weeks of freeze up features wide variations, though this relationship becomes more regular over time. Estimates of the effective thermal diffusivity are given for different seasons. The main periods in the variations in the heat content of water column in early winter are estimated.     

Temperature and Pressure Dependencies of Thermal Transport Properties of Rocks: Implications for Uncertainties in Thermal Lithosphere Models and new Laboratory Measurements of High-Grade Rocks in the Central Fennoscandian Shield

Measurements on thermal conductivity and diffusivity as functions of temperature (up to 1150 K) and pressure (up to 1000 MPa) are presented for Archaean and Proterozoic mafic high-grade rocks metamorphosed in middle and lower crustal pressures, and situated in eastern Finland, central Fennoscandian Shield. Decrease of 12–20% in conductivity and 40–55% in diffusivity was recorded between room temperature and 1150 K, which can be considered as typical of phonon conductivity. Radiative heat transfer effects were not detected in these samples. Pressure dependencies of the samples are weak if compared to crystalline rocks in general, but relatively typical for mafic rocks.The temperature and pressure dependencies of thermal transport properties (data from literature and the present study) were applied in an uncertainty analysis of lithospheric conductive thermal modellings with random (Monte Carlo) simulations using a 4-layer model representative of shield lithosphere. Model parameters were varied according to predetermined probability functions and standard deviations were calculated for lithospheric temperature and heat flow density after 1500 independent simulations. The results suggest that the variations (uncertainties) in calculated temperature and heat flow density values due to variations in the temperature and pressure dependencies of conductivity are minor in comparison to the effects produced by typical variations in the room temperature value of conductivity, heat production rate or lower boundary condition values.     

Evaporation and energy balance of a sub‐Arctic hillslope in northern Finland

This paper presents measurements of the energy balance (radiation, sensible heat flux, evaporation) from a sub‐arctic hillside in northern Finland for a summer season. Comparisons are also made with a nearby wetland site. The hillslope measurements show an equal partition of the radiant energy into sensible and latent heat flux. The evaporative ratio of just over one half was remarkably constant throughout the season, despite very large day‐to‐day and diurnal variations of temperature, humidity deficit and radiation input. This conservative behaviour of the evaporation was caused by a strong rise in effective surface resistance to evaporation with increasing vapour pressure deficit. This suggests a strong physiological control on the evaporation, with stomata closing at times of high evaporative demand. There was no obvious impact of soil‐water stress on the evaporation. However, a comparison with the evaporation measured at a nearby mire site in 1997 suggests that the mire has a significantly lower surface resistance, even when the impact of a significantly lower humidity deficit in the earlier year is taken into account. The measurements are used to test, off‐line, the performance of MOSES (Meteorological Office Surface Exchange Scheme), a simple, but comprehensive, land surface model. The sensitivity of the energy exchanges to the thermal properties of the top soil layer (a surrogate for the upper soil/vegetation layer) is investigated with the use of the model. It is found that the evaporation is insensitive to these properties; they do, however, influence the partition of energy between the sensible heat flux and the ground heat flux (and hence the soil temperatures). It is suggested that the model needs to represent the thermal properties of the canopy more realistically. Copyright © 2002 John Wiley & Sons, Ltd.     

The thermal diffusivity of soil at tropical stations in southern hemisphere

Summary The study of heat transfer or temperature changes in the surface layers of the soil are important in agricultural science at tropical latitudes. The quantity, thermal diffusivity largely determines the temperature changes produced in the layer of the soil when heat is conducted there from an adjacent layer. Therefore, the authors have determined the thermal diffusivity of the soil at the sites Arapongas (23.5°S, 51.7°W) and São José dos Campos (23.3°S, 45.8°W), in Brazil (South America), in accordance with the simple theory of periodic heat flow in a one dimensional, semiinfinite, homogeneous medium. The diffusivity increases with the increase of moisture content in the surface layers of the soil. The results of diffusivity obtained from these methods agree well with those of past workers obtained by other techniques.     

青藏高原北部活动层土壤热力特性的研究

利用2003年10月～2004年9月期间高原北部可可西里(QT01)、北麓河(QT02)、开心岭(QT05)、通天河(QT06)等地活动层土壤温度梯度、土壤热通量及土壤水分的观测资料,计算了高原北部活动层土壤的导热率、土壤容积热容量、导温率等土壤热力参数.结果显示,QT02、QT05、QT06三站导热率、导温率夏秋季节较大而冬季较小,容积热容量则相反,表现为秋冬季节大而夏季较小;QT01站导热率表现为春季大,夏季较小;表层土壤粒度较小及较低的土壤湿度是冬季导热率较小的可能原因;冻土的热力特征参量可描述为相应深度的温度、体积含冰量及土壤盐度的函数,土壤含水量是融土热特征参数的主要影响因子;土壤水分含量小于某一临界值时,导温率随土壤水分含量的增大而增大,反之则减小.     

The distribution of thermal diffusivity in the Earth's crust

Data in the literature and additional measurements on the thermal diffusivities of granites, granulites and ultrabasic rocks at temperatures up to 1000 K and pressures to 2 GPa, have been used to propose a new model for thermal diffusivity distribution in the crust and upper mantle.The laboratory measurements were made using a pulse method or the Angstroem method with cylindrical heat flow. After making particular assumptions about the pressure and temperature distribution within the top 60 km the pressure and temperature dependencies of diffusivity were transformed into a depth dependence.The model is characterised by a continuous decrease of diffusivity to a depth of ～30 km where there is a small but rapid increase to a nearly constant value of 7.3 × 10^?3 cm² s^?1.     

Determining thermal diffusivity using near‐surface periodic temperature variations and its implications for tracing groundwater movement at the eastern margin of the Tibetan Plateau

The thermal diffusivity is the key parameter that controls near‐surface temperature where periodic temperature variation is progressively attenuated and delayed with depth. This article presents the results of apparent thermal diffusivity using temperatures recorded by a bedrock temperature measurement network in the fault zones of western Sichuan. High sensitivity temperature sensors (10^?4 K) were installed at a maximum depth reaching 30 m. The apparent thermal diffusivities were deduced from both amplitude damping and phase shifting of annual temperature variations between two different depths. Under pure conduction, the thermal diffusivity determined through the phase method (α_Φ) should be equivalent to that determined through the amplitude method (α_A), whereas effects of the upward (downward) water flow are evidently reflected in the amplitude decay to make α_Φ larger (lesser) than α_A. The discrepancy between α_Φ and α_A can thus be a tracer of water movement or convective heat transfer. The calculated α_Φ of the measurement stations varies from 1.22 × 10^?6 to 3.00 × 10^?6 m²/s, and the estimated α_A ranges from 0.93 × 10^?6 to 2.41 × 10^?6 m²/s. Two regimes of heat transfer underground were suggested from the results. Conductive heat transport prevails over the nonconductive processes at five stations, which is characterized by α_Φ coincident with α_A for the same depth pair. On the contrary, the values of α_Φ differ from α_A at six stations in the intersection area of the Y‐shaped fault system, implying that convective heat transfer also plays a comparably important role. This finding is consistent with the hot springs distribution of the area. The results also indicate that water moves upward with an average Darcy velocity of approximately ?1 × 10^?7 m/s in this region. Our research provides new evidence for the hydrothermal activity in the fault zones at the eastern margin of the Tibetan Plateau.     

The thermal diffusivity of red sandy soil at Waltair

Summary The study of heat exchanges or temperature changes in the surface layers of the soil are important in agricultural science at tropical latitudes. The quantity, thermal diffusivity largely determines the temperature change produced in any layer of the soil when heat is conducted there from an adjacent layer. Therefore, the authors have determined the thermal diffusivity of the soil from range and lag methods suggested byJohnson andDavies [15]²) andCoutis [7] respectively. The values of diffusivity cbtained from these methods agree well with each other. The effect of soil moisture on diffusivity has been studied. The diffusivity increases with the increase of moisture in the surface layers of the scil. The ratio of ranges of soil temperature at different depths is found to be approximately constant which is in agreement with the theory of heat flow into the soils. The results of diffusivity obtained from these methods agree well with those results of past workers. The mean value of the thermal diffusivity of red sandy soil at the experimental site of Waltair is found to be 6.336×10^–3 cm²/sec.     

Evolution of double diffusion convection in a felsic magma chamber

The onset of double diffusion convection (DDC) is modeled in a two-dimensional case in respect to magma chambers. The viscosity model for the melt takes into account the effects of temperature and concentration of the dissolved component (H₂O). The upper boundary of the convecting magma chamber is assumed to be anhydrous and at constant temperature, whereas the lower boundary is treated as being hydrous permeable with a temperature greater than that within the upper boundary. The case of positive compositional and thermal buoyancy of melt is studied assuming a H₂O diffusion coefficient small in comparison with thermal diffusivity. The DDC has been modeled using a system of equations solved by the finite difference method on a square grid. The convective pattern evolution has been studied for fixed boundary conditions as well as for cooling and degassing. Due to the higher viscosity in the upper zone, the upper boundary layer is thicker than the lower one. The variation of water concentration in this zone of the convective cell can be significant. In nature, the high gradient of water concentration can be responsible for the observed variations of water content in minerals crystallized from a granite melt (e.g., biotite). Because of a high Lewis number (= 100), temperature variations in the magma chamber decay much faster than the water concentration. In this case the intensive convection can continue at a constant temperature due to the non-zero water content in the chamber. In principle, the effect can be applied to the formation of magmatic bodies. If the cooling and degassing system reaches a uniform temperature distribution prior to the crystallization temperature, water content throughout the body may still remain variable.     

Near‐surface temperatures and heat balance of bare outcrops exposed to solar radiation

Subsurface temperatures in rocks naturally fluctuate under the influence of local meteorological conditions. These fluctuations play a role in mechanical weathering, thus creating the environmental conditions conducive to natural hazards such as rockfalls and providing important sediment source terms for landscape evolution. However, the physics that control heat penetration into rocks are not fully understood, which makes the underground thermal state difficult to interpret when temperature measurements are available and even more difficult to estimate for unmonitored sites. This is an important lacuna given possible impacts of future climate change on mechanical weathering processes. The natural daily variations of subsurface temperatures were investigated on a bare gneiss outcrop exposed to solar radiation, where temperatures at various depths (up to 50 cm), as well as the solar radiation reaching a pyranometer, were monitored hourly for several months. This detailed times series of thermal data was used to gain insight into the heat balance at the inclined free surface of the rock mass. Attention was focused on two major contributors to the heat balance; the heat flux entering the rock mass through conduction and the incoming shortwave (solar) radiation. A Fourier decomposition of the temperature measurements provided an estimate of the in situ thermal conductivity of the rock and was used to calculate the conductive term. The shortwave radiation term was determined on the basis of the pyranometer measurements adjusted to account for the angle of incidence of the sun. It is shown that, throughout clear‐sky periods, heat exchanges at the surface are mainly controlled by direct solar radiation during the day, and by a roughly constant outgoing heat flux during the night. Subsurface temperatures can be reliably estimated with a semi‐infinite medium model whose boundary condition is derived from an analytical insolation model that takes atmospheric attenuation into account. Copyright © 2011 John Wiley & Sons, Ltd.     

Thermal conductivity in a vadose zone: A novel spectral solution and application by the implication of significant coherence of thermal condition in the shallow soil water layer

In the context of the heterogeneity in the unsaturated or vadose zone, accurately representing the analytical mechanisms and in-situ water content within the soil layer poses a significant challenge. Particularly in shallow layers, thermal conditions exhibit rapid changes in response to evolving surface temperatures. This study proposes a hypothesis suggesting that the in situ heat mechanism may notably impact the soil water layer. The research introduces an innovative approach to theoretically uncover thermal conditions, including soil temperature, soil temperature gradients, and heat flux, within the shallow Quaternary gravel layer at various depths through spectral analysis of temporal observations. The study presents a stochastic inverse solution to estimate thermal conductivity by leveraging spectral analysis of soil heat flux and temperature gradients. The findings reveal that thermal conditions exhibit the most prominent periodic fluctuations during the diurnal process over a 24-hour cycle. The soil temperature gradients and heat flux measurements at depths of 0.1, 0.3, 0.6, and 1.2 m demonstrate their ability to capture changes in soil temperature and air temperature to a certain extent within the frequency domain. Furthermore, the analysis highlights the intrinsic uncertainty and sensitivity of estimating thermal conductivity in heterogeneous soil environments. The wide variability observed in thermal conductivity values, coupled with their dependence on soil type and environmental conditions, underscores the need for careful consideration of these factors in future studies and modeling efforts. Applying the derived inverse spectral solution allows for determining thermal conductivity throughout the soil-water system across depths ranging from 0.1 to 1.2 m. As a result, this research demonstrates the feasibility and practicality of assessing the thermal conductivity of the soil layer in conjunction with heat flux and temperature gradients through spectral analysis.     

Thermische Energieflüsse an der Wasseroberfläche: Beispiel Sempachersee

Data collected every 20 minutes for 18 months by a meteorological buoy moored on Lake Sempach in Switzerland (maximum depth 86 m, surface area 14.1 km²) are used to calculate different processes contributing to the net heat flux between water and atmosphere. The processes considered are shortwave and longwave radiation, evaporation/condensation and sensible heat transfer. The temporal resolution of the measurements allows the evaluation of the processes occurring on three different time scales: diurnal variations, weather events of a few days and yearly cycles. The heat content of the lake is calculated from quasi-continuous measurements of water temperature at different depths. The yearly amplitude of the heat content is 1100·10⁶ J/m². Short-time variations of the heat flux determined from water temperature analysis agree well with the flux variations modeled using meteorological data. However, the latter generally underestimates the measured net heat flux in the long term. Wind measurements, together with the net heat flux, are used to calculate the Flux Richardson Number and the Monin-Obukov Length. Examples are given to show the predominant influence of the wind on the stratification of the upper water column and thus on the surface water temperature.      

Thermal characterization of the Vulcano fumarole field

Ground-based thermal infrared surveys can contribute to complete heat budget inventories for fumarole fields. However, variations in atmospheric conditions, plume condensation and mixed-pixel effects can complicate vent area and temperature measurements. Analysis of vent temperature frequency distributions can be used, however, to characterise and quantify thermal regions within a field. We examine this using four thermal infrared thermometer and thermal image surveys of the Vulcano Fossa fumarole field (Italy) during June 2004 and July 2005. These surveys show that regions occupied by low temperature vents are characterised by distributions that are tightly clustered around the mean (i.e., the standard deviation is low), highly peaked (positive kurtosis) and skewed in the low temperature direction (negative skewness). This population is associated with wet fumaroles, where boiling controls maximum temperature to cause a narrow distribution with a mode at 90–100°C. In contrast, high temperature vent regions have distributions that are widely spread about the mean (i.e., the standard deviation is high), relatively flat (negative kurtosis) and skewed in the high temperature direction (positive skewness). In this dry case, fumaroles are water-free so that maximum temperatures are not fixed by boiling. As a result greater temperature variation is possible. We use these results to define two vent types at Vulcano on the basis of their thermal characteristics: (1) concentrated (localized) regions of high temperature vents, and (2) dispersed low temperature vents. These occur within a much larger region of diffuse heat emission across which surfaces are heated by steam condensation, the heat from which causes elevated surface temperatures. For Vulcano's lower fumarole zone, high and low temperature vents occupied total areas of 3 and 6 m², respectively, and occurred within a larger (430 m²) vent-free zone of diffuse heat emission. For this lower zone, we estimate that 21–43 × 10³ W of heat was lost by diffuse heat emission. A further 4.5 × 10³ W was lost by radiation from high temperature vents, and 6.5 × 10³ W from low temperature vents. Thus, radiative heat losses from high and low temperature vents within Vulcano's lower fumarole zone respectively account for 10% and 15% of the total heat lost from this zone. This shows that radiation from open vents can account for a non-trivial portion of the total fumarole field heat budget.     

Exploration of regional surface average heat flow from meteorological and geothermal series

We attempt to compute the Surface Average Heat Flow （SAHF） from long-term temperature observations of one hundred seventy-seven observational points at the depths of 0.8, 1.6, and 3.2 m, which were relatively evenly distributed in mainland China. We first employ Fourier transformation to remove the influence of atmospheric temperature variations from the observation series, which are classified into the type of the steady-state temperature monotonously increasing with depth （type I） and other three types. Then we compare our results obtained from the data of type I, of which the values are thought to equal to those of the mean borehole heat flow, with those obtained from traditional heat flow observations mainly distributed in North China Craton. In computations of the SAHF at the observation stations, we deduce the thermal diffusivity and volumetric specific heat of the soil by employing harmonic solutions of the heat conduction equation for the same moisture group as the first step, and then we determine the SAHF using Fourier＇s law. Our results indicate that the SAHF derived from shallow earth geothermal data can reflect the heat flow field to a large extent.     

Bulk density effects on soil hydrologic and thermal characteristics: A numerical investigation

Soil bulk density (ρ_b) is commonly treated as static in studies of land surface dynamics. Magnitudes of errors associated with this assumption are largely unknown. Our objectives were to (a) quantify ρ_b effects on soil hydrologic and thermal properties and (b) evaluate effects of ρ_b on surface energy balance and heat and water transfer. We evaluated 6 soil properties, volumetric heat capacity, thermal conductivity, soil thermal diffusivity, water retention characteristics, hydraulic conductivity, and vapour diffusivity, over a range of ρ_b, using a combination of 6 models. Thermal conductivity, water retention, hydraulic conductivity, and vapour diffusivity were most sensitive to ρ_b, each changing by fractions greater than the associated fractional changes in ρ_b. A 10% change in ρ_b led to 10–11% change in thermal conductivity, 6–11% change in saturated and residual water content, 49–54% change in saturated hydraulic conductivity, and 80% change in vapour diffusivity. Subsequently, 3 field seasons were simulated with a numerical model (HYDRUS‐1D) for a range of ρ_b values. When ρ_b increased 25% (from 1.2 to 1.5 Mg m^?3), soil temperature variation decreased by 2.1 °C in shallow layers and increased by 1 °C in subsurface layers. Surface water content differed by 0.02 m³ m^?3 for various ρ_b values during drying events but differences mostly disappeared in the subsurface. Matric potential varied by >100 m of water. Surface energy balance showed clear trends with ρ_b. Latent heat flux decreased 6%, sensible heat flux increased 9%, and magnitude of ground heat flux varied by 18% (with a 25% ρ_b increase). Transient ρ_b impacted surface conditions and fluxes, and clearly, it warrants consideration in field and modelling investigations.     

A THREE-DIMENSIONAL NUMERICAL BOTTOM-HOLE TEMPERATURE STABILIZATION MODEL*

The heat flow equation in cylindrical coordinates is solved numerically for any general distribution of thermal diffusivity. The temperature stabilization of a borehole is considered, and solutions for the case where thermal diffusivity is a function of radial distance from the borehole are obtained and compared to solutions for uniform diffusivity. The results are discussed in terms of thermal diffusivities that are different for the well contents and for the surrounding material. It is found that the approach to formation temperature is affected by differences between well contents and the surrounding region.     

Thermal Monitoring of Natural Source Zone Depletion

Natural depletion of subsurface petroleum liquids releases energy in the form of heat. The rate of natural source zone depletion (NSZD) can be derived from subsurface temperature data. An energy balance is performed to resolve NSZD‐generated energy in terms of W/m². Biodegradation rates are resolved by dividing the NSZD energy by the heat of reaction in joules/mol. Required temperature data are collected using data loggers, wireless connections, and automated data storage and analysis. Continuous thermal resolution of monthly NSZD rates at a field site indicates that apparent monthly NSZD rates vary through time, ranging from 10,000 to 77,000 L/ha/year. Temporal variations in observed apparent NSZD rates are attributed to processes governing the conversion of CH₄ to CO₂, as opposed to the actual rates of NSZD. Given a year or more of continuous NSZD rate data, it is anticipated that positive and negative biases in apparent NSZD rates will average out, and averaged apparent NSZD rates will converge to true NSZD rates. An 8.4% difference between average apparent NSZD rates over a 31‐month period using the thermal monitoring method and seven rounds of CO₂ efflux measurements using CO₂ traps supports the validity of both CO₂ trap and thermal monitoring methods. A promising aspect of thermal monitoring methods is that continuous data provide a rigorous approach to resolving the true mean NSZD rates as compared to temporally sparse CO₂ trap NSZD rate measurements. Overall, a vision is advanced of real‐time sensor‐based groundwater monitoring that can provide better data at lower costs and with greater safety, security, and sustainability.     

下扬子区地温场和大地热流密度分布

根据下扬子区５０余口井温测量资料，从中选取能代表地层温度的井温数据计算地温梯度，在实验室中测量中、新生界的１１０余块砂岩和泥岩热导率及古生界碳酸岩和砂岩１００余块露头样品的热导率．在此基础上，确定了４１口井的大地热流密度值．地温梯度和大地热流密度分布表明，下扬子大部分地区中生代构造热事件伴随的热异常已不明显，而新生代时期岩石层拉张地区─－苏北盆地和郯庐断裂带是高热流密度和高地温梯度区．