Subsurface Heat Flux Research Articles

Application of a soil temperature model for simulating the effect of dis-trict heating pipes on drinking water pipelines

According to Dutch legislation the drinking water temperature is required to be below 25°C at the tap to meet legionella prevention [1]. This requirement possibly limits the storage of heat in the subsoil and the transport of heat through pipelines. In order to asses the impact of heat transport pipelines on the drinking water temperature in adjacent drinking water pipelines, a soil temperature model was developed. This coupled micro-climate [2] and heat transport model relates atmospheric conditions to the temperature distribution in the sub-surface [3]. The subsurface part of the model is based on a finite element discretization of the transient heat conduction equation in a single phase material. The coupling of the subsurface part of the model with atmospherical part of the model requires that the sensible heat flux, the latent heat flux, net radiation and the subsurface heat flux are in equilibrium at the land surface. Simulation periods of a number of years are discritized in time steps of one hour. The model is validated by comparing the model results with a large number of field measurements in the Dutch city Rotterdam-Kralingen [3].
 The validated model is used to predict the drinking water temperature in transport, primary and secondary pipeline networks. The transport networks supply heat and water to the primary networks. Primary networks distribute their heat and water to secondary networks that transport it to buildings.
 with and without heating pipelines parallel to drinking water pipelines, with a limited flow of drinking water. The inner diameter of the heat supply and return pipelines, which are usually located close to each other, is 160.3 mm. The heat supply temperature is 90°C and the return temperature is 70°C. The inner diameter of the drinking water pipelines is 152 mm. The heat transport pipelines consist of an inner steel pipe with a wall thickness of 4 mm, a PUR isolation of 56 mm and a PE sleeve of 4 mm. The finite element discretization captures the geometry of the insulated pipeline and associated effective thermal properties. Drinking water pipelines have a PVC wall with a thickness of 4 mm. The drinking water pipeline cover depth is 1.00 m, the distance in between the drinking water pipeline and heat return pipeline is 0.75 m and the soil cover of the heat supply pipelines is 1.00 m. Tiles cover a dry sandy soil for which the specific heat capacity is 800 J/kgK, the thermal conductivity is 1.6 W/mK and the density of the soil is 1600 kg/m3. The figure shows a seasonal variation of the drinking water temperature of 13.8°C and an increase of the drinking water temperature due to the presence of the heat transport pipelines of 2.0°C, which is almost constant throughout the year. The maximum drinking water temperature is found in August and amounts to 23.8°C if the heat pipelines are absent and 25.8°C if they are present.
 Table 1 presents the results of a study with variation of the drinking water pipeline soil cover, the distance in between drinking water pipeline and heat return pipeline and the soil cover of the heat supply pipelines. Based on this table decisions can be made on the type of construction and the effect of the heat transport pipelines on adjacent drinking water pipelines.
 The table shows that the cover depth of the drinking water pipeline strongly influences the increase of the drinking water temperature due to atmospheric conditions. A decrease of the soil cover from 2.00 m to 0.75 m raises the maximal temperature by 4.2°C. The presence of the heat transport pipelines increases the temperature of the drinking water by 1.7°C for the case of a small cover depth and 2.1°C for a large cover depth. A decrease of the distance in between the drinking water pipeline and the heat return pipeline from 2.5 m to 0.25 m raises the maximal drinking water temperature by 2.6 °C. The calculation results show that the drinking water temperature is not sensitive to the proposed cover depth variation of the heat supply pipelines. The computational results for all networks considered, are collected in an expert tool that can be accessed via: https://www.tkiwatertechnologie.nl/projecten/opwarming-van-drinkwater/.

Surface energy balance on a polythermal glacier, Arctic, and the role of poleward atmospheric moisture transport

In recent years, increasing moisture over the Arctic and subarctic regions shows that the Arctic is experiencing wetting conditions, and poleward atmospheric moisture transport (PAMT) plays a vital role in the atmosphere-ice/snow interactions in the Arctic. To identify the effect of PAMT on the surface energy balance (SEB) for the Arctic glacier, meteorological data from an automatic weather station (AWS) at 377 m a.s.l. on the Austre Lovénbreen glacier, as well as the ERA5 reanalysis data from 30 April 2014 to 30 April 2015, were analyzed in this paper. Our results show that the net shortwave radiation (Snet) (18 W m−2, 55%), turbulent sensible (H) (14 W m−2, 43%) and subsurface heat flux (G) (1 W m−2, 2%) act as the energy sources, while the net longwave radiation (Lnet) (−19 W m−2, 56%), melt energy (Qm) (−12 W m−2, 35%) and turbulent latent heat flux (LE) (−3 W m−2, 9%) represent the heat sink. The development process of Atmospheric River (AR), primary form of PAMT, near the Svalbard in February 2015 was revealed according to the total column water vapor, 850 hPa winds and geopotential height fields. Compared to summer, the glacier SEB was more affected in winter by PAMT, leading to a frequent overcast and thus increasing air temperature, moisture, and wind speed, all of which are variables governing the SEB by decreasing H, LE and G less than increasing the Lnet. Our findings obtained here can help to better understand the diverse SEB change on the high Arctic glacier from the perspective of PAMT and large-scale atmospheric circulations anomalies.

Fault Zone Hydraulic Parameter Estimation by Passive Methods Using Natural Forces

AbstractHydrogeological conditions within fracture zones control subsurface fluid, solute, and heat flux and storage. While conventional groundwater methods using induced disturbances often require elaborate and expensive equipment, passive methods that use observed responses of groundwater levels to atmospheric pressure and Earth tides provide the opportunity to estimate hydrogeologic properties without having to conduct field testing. We present estimates of hydraulic properties of a fault‐damage zone embedded within crystalline rock using responses to natural perturbations, and then compare these to estimates obtained using conventional methods. We calculate the skin factor using the exhaustive algorithm to improve the consistency between the tidal and conventional methods and compare it with different barometric‐response methods in the frequency and time domains. For the tidal method, the hydraulic conductivity is 16% larger than the estimate obtained from a conventional aquifer test, the barometric‐response method in the frequency domain is 6% larger, and the inverse, Hvorslev's, CBP, and Valois's methods in the time domain are, respectively, 71%, 72%, and 97% smaller and 624% larger. Estimated fault‐damage zone properties yield a hydraulic diffusivity of D ≈ 3 m2 s−1 and a permeability of k ≈ 4 × 10−13 m2 (0.4 Darcy), which confirms the presence of a highly damaged zone. The combined tidal‐ and barometric‐response methods provide a new and robust approach for understanding and characterizing hydrogeological properties of fault‐damage zones.

City-wide monitoring and contributing factors to shallow subsurface temperature variability in Nanjing, China

Shallow temperatures down to a depth of 100 m were measured over one year in 19 closed boreholes located in Nanjing, China, to reveal the conditions and factors influencing the subsurface thermal regime. A monitoring concept with distributed temperature sensing, fiber Bragg grating-based sensor, and a type of Resistance Temperature Detectors, is implemented, providing spatial distribution characteristics of subsurface temperatures. The results show that temperatures near the surface are most dynamic, influenced by the air temperature. The temperature remains stable at the depth of 10–20 m. The mean transition temperature is 18.1 °C. Borehole measurements are interpolated by using satellite images and surface temperature records to obtain large-scale surface temperature distributions and temporal variations of subsurface temperature. Geological and hydrological conditions are primary factors by affecting subsurface upward heat flux and heat loss. Urban land cover change and enhanced heat release from urbanization contribute to a subsurface urban heat island with intensities of 1.0–4.4 °C. The altered subsurface thermal regime is of primary concern for the management of shallow geothermal energy use. The monitoring concept in this study can provide spatially-temporally continuous profiles of subsurface temperature and become a reference for city-wide geothermal monitoring in other urban areas.

Size determination of interior defects by reconstruction of subsurface virtual heat flux for step heating thermography

Step heating thermography is a non-destructive testing (NDT) technique that inspects interior defects by observing surface temperature rises during a long pulse heat stimulation. Due to the heat diffusion induced blurring of defect shapes, it is a challenging task to accurately determine the sizes of deep and small defects. This work focuses on estimating the size of a subsurface defect by an inversion of temperature images for the step heating thermography, to overcome the information loss during the propagation of thermal waves. We assume a space- and time-dependent virtual heat flux on the defect surface, which is reconstructed from surface temperature measurements by solving a two-dimensional inverse heat conduction problem. The local future time concept is combined with the Tikhonov's regularization to stabilize the inverse solution. A prudent choice of the regularization parameter is carried out through the L-curve. The feasibility of the proposed approach is assessed by numerical simulations and experiments. It is shown that the inversion brings an improvement in defect sizing accuracy for defects with low width-to-depth ratios and an efficient suppression of measurement noises.

Influence of the ocean on tropical cyclone intensity using a high resolution coupled atmosphere–ocean model: A case study of very severe cyclonic storm Ockhi over the North Indian Ocean

AbstractA very severe cyclonic storm (VSCS), Ockhi was conceived in the Bay of Bengal and moved over the Arabian Sea undergoing rapid intensification (RI) in the early stages of its life cycle. Ockhi is simulated using the high‐resolution coupled Hybrid Coordinate Ocean Model and the Hurricane Weather Research Forecast model. The study suggests that sea surface temperature warmer than the seasonal climatological mean with the availability of a large tropical cyclone heat potential (TCHP) has acted as a potential cause for RI when the TC moved over that region. We have conducted experiments with (CP) and without (UCP) ocean coupling. The predicted tracks of UCP and CP experiments agree well with the India Meteorological Department's best track data. However, CP showed a significant improvement in intensity prediction with 61 and 19% for mean sea level pressure and maximum sustained surface wind at 10 m respectively in comparison to UCP. The presence of thermal and haline stratification in the subsurface affects surface cooling. The subsurface turbulent heat flux calculated for the high‐TCHP region under the TC suggests that the upward transport of heat, which increases the enthalpy flux, becomes necessary to bring about RI. The primary circulation, secondary circulation, inflow, thermal structure, moisture distribution and mass flux within the TC environment during the 24‐hr RI period are analyzed to investigate the evolution of TC characteristics for both UCP and CP experiments. The analyses suggest that the UCP experiments show higher values of intensity as compared to CP experiments. Further, a more organized evolution of updrafts is present in the CP simulation, maybe due to the formation of a stable boundary layer. The study shows the significant influence of coupling on surface enthalpy controlling boundary layer characteristics and thus ultimately producing a more organized TC.

Simulation and Scaling of the Turbulent Vertical Heat Transport and Deep-Cycle Turbulence across the Equatorial Pacific Cold Tongue

AbstractMicrostructure observations in the Pacific cold tongue reveal that turbulence often penetrates into the thermocline, producing hundreds of watts per square meter of downward heat transport during nighttime and early morning. However, virtually all observations of this deep-cycle turbulence (DCT) are from 0°, 140°W. Here, a hierarchy of ocean process simulations, including submesoscale-permitting regional models and turbulence-permitting large-eddy simulations (LES) embedded in a regional model, provide insight into mixing and DCT at and beyond 0°, 140°W. A regional hindcast quantifies the spatiotemporal variability of subsurface turbulent heat fluxes throughout the cold tongue from 1999 to 2016. Mean subsurface turbulent fluxes are strongest (∼100 W m−2) within 2° of the equator, slightly (∼10 W m−2) stronger in the northern than Southern Hemisphere throughout the cold tongue, and correlated with surface heat fluxes (r2= 0.7). The seasonal cycle of the subsurface heat flux, which does not covary with the surface heat flux, ranges from 150 W m−2near the equator to 30 and 10 W m−2at 4°N and 4°S, respectively. Aseasonal variability of the subsurface heat flux is logarithmically distributed, covaries spatially with the time-mean flux, and is highlighted in 34-day LES of boreal autumn at 0° and 3°N, 140°W. Intense DCT occurs frequently above the undercurrent at 0° and intermittently at 3°N. Daily mean heat fluxes scale with the bulk vertical shear and the wind stress, which together explain ∼90% of the daily variance across both LES. Observational validation of the scaling at 0°, 140°W is encouraging, but observations beyond 0°, 140°W are needed to facilitate refinement of mixing parameterization in ocean models.Significance StatementThis work is a fundamental contribution to a broad community effort to improve global long-range weather and climate forecast models used for seasonal to longer-term prediction. Much of the predictability on seasonal time scales is derived from the slow evolution of the upper eastern equatorial Pacific Ocean as it varies between El Niño and La Niña conditions. This study presents state-of-the-art high-resolution regional numerical simulations of ocean turbulence and mixing in the eastern equatorial Pacific. The results inform future planning for field work as well as future efforts to refine the representation of ocean mixing in global forecast models.

Two-layer transient heat transfer using impulse response methods

Solutions to the inverse heat conduction problem (IHCP) are methods that can be used to quantify surface heat flux in multi-layer materials for components in which there are limited subsurface (internal) temperature measurements, such as coated components. A critical consideration is to capture high frequency fluctuations using a practical heat flux sensor. To that end, this paper highlights key parameters for calculating accurate surface heat transfer. Specifically, this research extends the available solutions to the IHCP for multi-substrate structures through an impulse response methodology. The sensitivity of the impulse method was quantified with respect to practical measurements. When compared to the inverse case, the impulse method resulted in lower errors when calculating surface heat flux over a range of conditions. Overall, this work provides a foundation for deducing heat flux from a subsurface heat flux sensor while maintaining a high-frequency response.

On the importance of subsurface heat flux for estimating the mass balance of alpine glaciers

Glaciers, as massive freshwater reservoirs, support the planet's living systems and have an impact on our daily lives, even for communities living far away. Ongoing and future climate change is predicted to have strong impacts on the mass balance of alpine glacier around the world. To understand the relationship between climate and glacier dynamics, a range of mass balance models are currently used. Most of these models however, ignore subsurface heat fluxes as a component of glacier mass balance. Here, we set out to investigate the importance of subsurface heat flux for the mass balance of an alpine glacier using a surface energy mass balance model (SEM) coupled with a multilayer subsurface heat conduction model (MSHCM) that resolves the subsurface glacier temperature. As a case study, we investigate the Urumqi Glacier No.1 in the Tianshan Mountains (NW China), which has a long and continuous time series of surface and subsurface glacier temperature measurements. We evaluate the results of both glacier temperature models (SEM and MSHCM) using these in situ observations and investigate the sensitivity of mass balance to five meteorological factors: air temperature, precipitation, incoming shortwave radiation, relative humidity, and wind speed. The mass balance of the glacier was simulated first by including the influence of subsurface heat flux, and second, the subsurface heat flux was neglected. Observed and simulated mass balance and the englacial temperature were found to be reasonably close in both cases. Furthermore, the mass balance was simulated with a zero surface temperature assumption, which resulted in a 6% overestimation of the summer ablation. We concluded that the mass balance of Urumqi Glacier No.1 was most sensitive to variations in temperature, followed by precipitation. Furthermore, our results show that subsurface heat flux in the ablation area can generally be neglected in estimating the mass balance of alpine glaciers during ablation season.

Semi-analytical solution for temperature rise in a heterogeneous half plane containing arbitrarily shaped inhomogeneities subjected to surface heating

Temperature rise caused by surface heating is responsible for thermal-related failures of heterogeneous material, such as composites and alloys, in manufacturing processes and tribology. This study presents a semi-analytical method (SAM) for temperature rise in a half plane involving dispersed inhomogeneities of arbitrary shape undergoing external heat load. Green functions and frequency response functions (FRFs) for subsurface heat flux induced by the applied heat load, as well as a set of formulas for influence coefficients correlating disturbed temperature rise and uniform eigen-temperature gradients inside a rectangular inclusion in a full plane, are derived. The rectangular inclusion solution in a full plane is treated as an elementary solution to solve disturbed temperature rise in a heterogeneous half plane involving arbitrarily shaped inhomogeneities, through implementing the equivalent inclusion method (EIM), the method of images and discretizing the total computation area into a good many rectangular elements with the same size. Results obtained by the SAM are consistent with those of the finite element method (FEM). Effects of inhomogeneity numbers, material properties, volume fractions, and velocities of the moving heat load on temperature rise are discussed in detail. HIGHLIGHTS Green functions and frequency response functions for heat flux in a half plane subjected to surface heating are obtained. Influence coefficients relating disturbed temperature rise and uniform rectangular inclusion in a full plane are derived. The elementary rectangular inclusion method is utilized to cope with problems for inhomogeneities of arbitrary shapes and distributions. Effects of inhomogeneity numbers, material properties, volume fractions, and velocities of the moving heat load on temperature rise are discussed.

Multidecadal polynya formation in a conceptual (box) model

Abstract. Maud Rise polynyas (MRPs) form due to deep convection, which is caused by static instabilities of the water column. Recent studies with the Community Earth System Model (CESM) have indicated that a multidecadal varying heat accumulation in the subsurface layer occurs prior to MRP formation due to the heat transport over the Weddell Gyre. In this study, a conceptual MRP box model, forced with CESM data, is used to investigate the role of this subsurface heat accumulation in MRP formation. Cases excluding and including multidecadal varying subsurface heat and salt fluxes are considered, and multiple polynya events are only simulated in the cases where subsurface fluxes are included. The dominant frequency for MRP events in these results, approximately the frequency of the subsurface heat and salt accumulation, is still visible in cases where white noise is added to the freshwater flux. This indicates the importance and dominance of the subsurface heat accumulation in MRP formation.

Martian core heat flux: Electrical resistivity and thermal conductivity of liquid Fe at martian core P-T conditions

The present-day Mars has no magnetic field which suggests that the heat carried out of its liquid core is largely driven by conduction. To constrain the heat flux from Martian core, we measured the temperature (T) dependent electrical resistivity of solid and liquid Fe devoid of contamination in large volume press at various fixed pressure (P) up to 22.5 GPa, corresponding to the P at the top of the Martian core. We also measured its P-dependent resistivity up to 22.5 GPa at room T. At a P range between 18 and 20 GPa, we observed a drop in the electrical resistivity of ~35 μΩcm which is attributed to a loss in long range order magnetic structure. This loss gives rise to an overall decrease in the electron scattering processes induced by magnon. The transition from long- to short-range order magnetic structure occurs in association with the completion of crystallographic transformation from α-bcc (ferromagnetic) to ε-hcp (paramagnetic). The decrease in the electrical resistivity at the same P range corresponds to an increase in thermal conductivity of ~30 Wm−1 K−1. The resistivity and thermal conductivity of liquid Fe at the Martian core mantle boundary (CMB) on the cores side are estimated to be ~68 ± 3 μΩcm and ~82 ± 3 Wm−1 K−1, respectively. The heat conducted along its core adiabat is found to be ~45 mW−1 m−2. With a core radius of ~1700 km, we obtain a value of 0.3 TW for its total surface heat flux. In comparison with the resistivity of Fe at the Earth's core conditions reported by a recent study, our result indicates that pure liquid Fe is electrically more conductive in the Martian core than in the Earth's core. Our results will complement the HP3 subsurface heat flux measurements in the on-going NASA InSight Mission.

A Test Study of an Energy and Mass Balance Model Application to a Site on Urumqi Glacier No. 1, Chinese Tian Shan

In this study, energy and mass balance is quantified using an energy balance model to represent the glacier melt of Urumqi Glacier No. 1, Chinese Tian Shan. Based on data from an Automatic Weather Station (4025 m a.s.l) and the mass balance field survey data nearby on the East Branch of the glacier, the “COupled Snowpack and Ice surface energy and Mass balance model” (COSIMA) was used to derive energy and mass balance simulations during the ablation season of 2018. Results show that the modeled cumulative mass balance (−0.67 ± 0.03 m w.e.) agrees well with the in-situ measurements (−0.64 ± 0.16 m w.e.) (r2 = 0.96) with the relative difference within 5% during the study period. The correlation coefficient between modeled and observed surface temperatures is 0.88 for daily means. The main source of melt energy at the glacier surface is net shortwave radiation (84%) and sensible heat flux (16%). The energy expenditures are from net longwave radiation (55%), heat flux for snow/ice melting (32%), latent heat flux of sublimation and evaporation (7%), and subsurface heat flux (6%). The sensitivity testing of mass balance shows that mass balance is more sensitive to temperature increase and precipitation decrease than temperature decrease and precipitation increase.

Assessing the role of oceanic heat fluxes on ice ablation of the central Chukchi Sea Shelf

We investigate the role of oceanic heat flux convergence in the summertime retreat of sea ice in the presence of a mean background flow. Prior studies indicated that eddies generated along the marginal ice zone front carry substantial quantities of heat laterally beneath the ice, but the direct importance of these fluxes to the summertime retreat of sea ice was not well established. We use the Regional Ocean Model System (ROMS) with an idealized configuration of the Chukchi Sea shelf and without wind forcing to: (1) determine the contributions to ice melt from the oceanic heat flux compared to that from the net atmospheric heat flux through the ice surface; (2) evaluate the role of mesoscale fluctuations versus the mean background flow in providing this sub-surface heat flux, and (3) evaluate the role of the underlying bathymetry in modifying the subsurface heat flux to the ice. Analyses show that the three main water masses (Melt Water, Bering Sea Water and Winter Water) establish frontal systems (the Shelf Water Front and the Ice Edge Melt Water Front) that control baroclinic processes, which in turn regulate the quantity of heat fluxed laterally and vertically to the ablating ice edge. We identify and characterize distinct oceanic zones associated with these fronts (the Shelf Water Transition Zone and the Melt Water Transition Zone) that are delineated by flow dynamics and hydrographic structure. The integrated heat flux along the modeled ice edge is significant: lateral eddy transport of heat is as large as 2 TW, of which 50% is fluxed upwards into the near-surface Melt Water. We introduce a parameterization for the vertical heat transport to the ice through the near-surface meltwater lens that is a function of the along-front current velocity and the cross-front temperature gradient. Such a parameterization could improve coarse-scale ocean and climate models that lack the resolution necessary for reproducing such small-scale processes. The results of this study may be informative to investigations of ice edge biological processes.

Measurements of turbulence transfer in the near-surface layer over the Antarctic sea-ice surface from April through November in 2016

AbstractThe surface energy budget over the Antarctic sea ice from 8 April 2016 through 26 November 2016 are presented. From April to October, Sensible heat flux (SH) and subsurface conductive heat flux (G) were the heat source of surface while latent heat flux (LE) and net radiation flux (Rn) were the heat sink of surface. Our results showed larger downwardSH(due to the warmer air in our site) and upwardLE(due to the drier air and higher wind speed in our site) compared with SHEBA data. However, the values ofSHin N-ICE2015 campaign, which located at a zone with stronger winds and more advection of heat in the Arctic, were comparable to our results under clear skies. The values of aerodynamic roughness length (z0m) and scalar roughness length for temperature (z0h), being 1.9 × 10−3m and 3.7 × 10−5m, were suggested in this study. It is found that snow melting might increasez0m. Our results also indicate that the value of log(z0h/z0m) was related to the stability of stratification. In addition, several representative parameterization schemes forz0hhave been tested and a couple of schemes were found to make a better performance.

Evaluation of an integrated sewage pipe with ground heat exchanger for long-term efficiency estimation

Extracting heat from a sewage pipe through a typical horizontal ground heat exchanger has recently been introduced as a renewable energy alternative to reduce fossil fuel usage. This paper presents a novel design for a ground heat exchanger that extracts heat from the surrounding soil and sewage within the pipe while simultaneously being carried to a wastewater treatment plant. This research focuses on the long-term efficiency of the system under transient conditions in a cold climate. A numerical model using COMSOL Multiphysics was developed to verify the sustainability of the system for over 25 years. The model used constant inlet fluid temperatures to evaluate heat transfer with convective pipe flow and conductive phase change within the soil. The results showed a maximum temperature change in the surrounding soil adjacent to the heat extraction system over 25 years was 0.10 °C during the heating season in Winnipeg, Manitoba. The distance at which the heat extraction system did not show an impact on temperature change of adjacent soil was determined at 4 m. Critical parameters in this evaluation were system depth, sewage level, and the high-density polyethylene pipe thermal properties. The sustainability of the system was not affected by the system depth due to thermal balancing between climatic, subsurface and sewage heat fluxes. Sustainable behavior was achieved at 50 % and 75 % of sewage pipe capacity. The effect on thermal performance from the high-density polyethylene pipe thermal properties was deemed insignificant.

Application of Tikhonov Regularization for 1D Geothermal Heat Flux Ill-Posed Inverse Problem: A Case Study on Chad Sedimentary Basin

Subsurface heat flux information is important in geothermal exploration. With the information, geophysicists can map exactly the thermal potential in a particular area. Based on the surface heat flux, inverse modeling produces the 1D subsurface heat flux distribution. However, inverse problems in the geothermal system are generally ill-posed. Small changes in the data can cause large changes in the solution and the solution may not be unique. To solve the mentioned non-linear and ill-posed equation above, Tikhonov regularization is a choice for stabilizing the inverse calculation. This paper demonstrates how Tikhonov regularization is useful to solve subsurface heat flux distribution both in the synthetic model and real model. Based on surface heat flux distribution from the direct problem, the preconditioned conjugate gradient algorithm calculates the subsurface heat flux. With the correct choice of the regularization parameter, the inverse model fits the initial model. For the testing purposes in real-world conditions, Chad sedimentary basin located in Chad and Nigeria is used as a model. A high geothermal gradient is found in this area. Therefore, geothermal explorations are on the rise recently. Its thermal conductivity, heat production, and stratigraphy data from previous researches provide information about the initial model. The heat flux curve generated from inversion matches the initial noisy model with the error of around 10−9 mW/m2. Therefore, to answer the increasing energy demand, this method can be highly applicable to future geothermal prospecting.

Construction of Deep Thermal Models Based on Integrated Thermal Properties Used for Geothermal Risk Management

The development of deep geothermal energy may be at risk from the economic point of view if the estimated deep thermal field is far from its real state. The strong heterogeneity of geological units makes it challenging to perform a reliable estimation on the construction of the deep thermal field over a large region. Additionally, the thermal properties of rocks, such as thermal conductivity and the radiogenic element concentration, whether they are from laboratory measurements or inversed from well logs, may strongly control the deep thermal field at a local scale. In this paper, the thermal conductivities of rocks from the Trois-Rivieres region in the Saint Lawrence Lowlands sedimentary basin in eastern Canada are obtained from two methods: (i) direct experimental measurement and (ii) indirect inversionmethod using well logs, including gamma ray, neutron porosity, density, and photoelectric absorption factor. The spatial distribution of subsurface temperature in the study area in the Trois-Rivieres region is numerically investigated by considering four case studies that include different values (minimum, average, and maximum) of the thermal properties by applying the Underworld simulator. The results show that thermal properties play a large role in controlling the subsurface temperature distribution and heat flux. The temperature difference can reach 15 °C in the basement, caused by the difference in thermal properties in the Trois-Rivieres region. The highest heat flux is found in the Trenton–Black River–Chazy groups, and the lowest heat flux is in the Potsdam group, which also has the highest thermal conductivity. Vertical heat flux does not change linearly with depth but is highly related to the thermal properties of specific geological formations. Furthermore, it does not have a positive correlation with the vertical temperature changes. This demonstrates that the assessment of the potential of deep geothermal energy depending merely on the surface heat flux may greatly overestimate or underestimate the geothermal capacity. Construction of the thermal models based on the integrated thermal properties from both the experimental measurement and well logs in this paper is useful in reducing the exploration risk associated with the utilization of deep geothermal energy.

Effect of Vegetation on the Energy Balance and Evapotranspiration in Tallgrass Prairie: A Paired Study Using the Eddy-Covariance Method

We carried out a paired study in tallgrass prairie to evaluate the influence of vegetation on the energy exchange and evapotranspiration. Two eddy-covariance systems were installed over two adjoining sites, one of which was denuded of vegetation, with the adjacent, control site kept undisturbed. Our year-long investigation shows that, for quantifying the ground surface heat flux, the soil heat storage above the soil plates is more important than the sub-surface soil heat flux, both temporally and in magnitude. The incorporation of the soil heat storage, therefore, is indispensable for energy balance closure in areas with short vegetation. At our control site, we observed a critical threshold of 0.17 m3 m−3 in the surface (top 0.3 m) soil water content, whereby the energy partitioning is significantly affected by the presence of the photosynthetically active vegetation when the surface soil water content is higher than this critical threshold. The pattern of energy partitioning approaches that of the treated site when the surface soil water content is lower than this threshold (during drought), because of the suppression of plant physiological activities. This threshold also applies to the surface conductance for water vapour at the control site, where yearly evapotranspiration is 728 ± 3 mm (versus 547 ± 2 mm for the treated site). Thus, the soil water content and presence of active vegetation are the key determinants of energy partitioning and evapotranspiration. Any land-cover changes or vegetation-management practices that alter these two factors may change the energy and water budgets in tallgrass prairie.

Subsurface Lateral Heat Flux within the Heterogeneous Surface of a Subtropical Wetland and Its Potential Contribution to Energy Imbalance

AbstractIn the eddy covariance technique, lateral heat fluxes in the atmosphere, surfaces, and subsurfaces are often ignored under the assumption of a homogeneous surface. Among lateral heat fluxes, the surface and subsurface fluxes, which might affect the surface energy balance closure over a heterogeneous surface, are less studied. Many wetlands are heterogeneous, with a mix of vegetated areas and shallow open water. This study examined the subsurface lateral heat fluxes between a reed bed and the adjacent water of a subtropical wetland in Hong Kong, China. An array of temperature and water-level sensors was installed in the soil of the reed bed and in the adjacent water. An eddy covariance system was also set up on the reed bed. The subsurface lateral heat fluxes were largest close to the interface of the reed bed and water and decreased as the distance from the interface increased, as expected. However, the subsurface lateral heat fluxes could not account for the energy imbalance because their magnitudes were relatively small and fluctuated in phase with the energy budget residuals during the winter months. The uncertainties of the turbulent fluxes and the lateral heat fluxes were estimated to be 10%–20% and 10%–30%, respectively. This study explored another potential reason behind the energy imbalance of the eddy covariance technique. The results enhance the understanding of water and energy exchanges between a terrestrial biotope and the surrounding water, which might further generate insights into the biochemical processes in wetlands.