Heat as a groundwater tracer in shallow and deep heterogeneous media: Analytical solution,spreadsheet tool,and field applications

Groundwater flow advects heat, and thus, the deviation of subsurface temperatures from an expected conduction‐dominated regime can be analysed to estimate vertical water fluxes. A number of analytical approaches have been proposed for using heat as a groundwater tracer, and these have typically assumed a homogeneous medium. However, heterogeneous thermal properties are ubiquitous in subsurface environments, both at the scale of geologic strata and at finer scales in streambeds. Herein, we apply the analytical solution of Shan and Bodvarsson ( 2004 ), developed for estimating vertical water fluxes in layered systems, in 2 new environments distinct from previous vadose zone applications. The utility of the solution for studying groundwater‐surface water exchange is demonstrated using temperature data collected from an upwelling streambed with sediment layers, and a simple sensitivity analysis using these data indicates the solution is relatively robust. Also, a deeper temperature profile recorded in a borehole in South Australia is analysed to estimate deeper water fluxes. The analytical solution is able to match observed thermal gradients, including the change in slope at sediment interfaces. Results indicate that not accounting for layering can yield errors in the magnitude and even direction of the inferred Darcy fluxes. A simple automated spreadsheet tool (Flux‐LM) is presented to allow users to input temperature and layer data and solve the inverse problem to estimate groundwater flux rates from shallow (e.g., <1 m) or deep (e.g., up to 100 m) profiles. The solution is not transient, and thus, it should be cautiously applied where diel signals propagate or in deeper zones where multi‐decadal surface signals have disturbed subsurface thermal regimes.     

Simulating the effects of geologic heterogeneity and transient boundary conditions on streambed temperatures — Implications for temperature-based water flux calculations

Analytical solutions to the one-dimensional heat transport equation for steady-state conditions can provide simple means to quantify groundwater surface water exchange. The errors in exchange flux calculations that are introduced when the underlying assumptions of homogeneous sediments and constant temperature boundary conditions are violated were systematically evaluated in a simulation study. Temperatures in heterogeneous sediments were simulated using a numerical model. Heterogeneity in the sediments was represented by discrete, binary geologic units. High contrasts between the hydraulic conductivities (K) of the geologic units were found to lead to large errors, while the influence of the structural arrangement of the units was smaller. The effects of transient temperature boundary conditions were investigated using an analytical equation. Errors introduced by transient boundary conditions were small for Darcy-velocities > 0.1 m d^− 1 in the period near maximum and minimum annual surface water temperatures. For smaller fluxes, however, errors can be large. Assuming steady-state conditions and vertical flow in homogeneous sediments is acceptable at certain times of the year and for medium to high exchange fluxes, but pronounced geologic heterogeneity can lead to large errors.     

A new analytical solution for assessing climate change impacts on subsurface temperature

Groundwater temperature is an important water quality parameter that affects species distributions in subsurface and surface environments. To investigate the response of subsurface temperature to atmospheric climate change, an analytical solution is derived for a one‐dimensional, transient conduction–advection equation and verified with numerical methods using the finite element code SUTRA. The solution can be directly applied to forward model the impact of future climate change on subsurface temperature profiles or inversely applied to produce a surface temperature history from measured borehole profiles. The initial conditions are represented using superimposed linear and exponential functions, and the boundary condition is expressed as an exponential function. This solution expands on a classic solution in which the initial and boundary conditions were restricted to linear functions. The exponential functions allow more flexibility in matching climate model projections (boundary conditions) and measured temperature–depth profiles (initial conditions). For example, measured borehole temperature data from the Sendai Plain and Tokyo, Japan, were used to demonstrate the improved accuracy of the exponential function for replicating temperature–depth profiles. Also, the improved accuracy of the exponential boundary condition was demonstrated using air temperature anomaly data from the Intergovernmental Panel on Climate Change. These air temperature anomalies were then used to forward model the effect of surficial thermal perturbations in subsurface environments with significant groundwater flow. The simulation results indicate that recharge can accelerate shallow subsurface warming, whereas upward groundwater discharge can enhance deeper subsurface warming. Additionally, the simulation results demonstrate that future groundwater temperatures obtained from the proposed analytical solution can deviate significantly from those produced with the classic solution. Copyright © 2013 John Wiley & Sons, Ltd.     

An analytical solution for describing the transient temperature distribution in an aquifer thermal energy storage system

A mathematical model is developed for predicting the temperature distribution in an aquifer thermal energy storage (ATES) system, which consists of a confined aquifer bounded from above and below by the rocks of different geological properties. The main transfer processes of heat include the conduction and advection in the aquifer and the conduction in the rocks. The semi‐analytical solution in dimensionless form for the model is developed by Laplace transforms and its corresponding time‐domain solution is evaluated by the modified Crump method. Field geothermal property data are used to simulate the temperature distribution in an ATES system. The results show that the heat transfer in the aquifer is fast and has a vast effect on the vicinity of the wellbore. However, the aquifer temperature decreases with increasing radial and vertical distances. The temperature in the aquifer may be overestimated when ignoring the effect of thermal conductivity. The temperature distribution in an ATES system depends on the vertical thermal conduction in the rocks and the horizontal advection and thermal conduction in the aquifer. The present solution is useful in designing and simulating the heat injection facility in the ATES systems. Copyright © 2010 John Wiley & Sons, Ltd.     

Data collection methodology for dynamic temperature model testing and corroboration

This article describes a data collection approach for determining the significance of individual heat fluxes within streams with an emphasis on testing (i.e. identification of possible missing heat fluxes), development, calibration and corroboration of a dynamic temperature model. The basis for developing this approach was a preliminary temperature modelling effort on the Virgin River in southwestern Utah during a low‐flow period that suggested important components of the energy balance might be missing in the original standard surface‐flux temperature model. Possible missing heat fluxes were identified as bed conduction, hyporheic exchange, dead zone warming and exchange and poor representation of the amount of solar radiation entering the water column. To identify and estimate the relative importance of the missing components, a comprehensive data collection effort was developed and implemented. In particular, a method for measuring shortwave radiation behaviour in the water column and an in situ method for separating out bed conduction and hyporheic influences were established. The resulting data and subsequent modelling effort indicate that hyporheic and dead zone heat fluxes are important, whereas solar radiation reflection at the water surface was found to be insignificant. Although bed conduction can be significant in certain rivers, it was found to have little effect on the overall heat budget for this section of the Virgin River. Copyright © 2009 John Wiley & Sons, Ltd.     

Coupled groundwater flow and heat transport simulation for estimating transient aquifer–stream exchange at the lowland River Spree (Germany)

Subsurface flow and heat transport near Freienbrink, NE Germany, was simulated in order to study groundwater–surface water exchange between a floodplains aquifer and a section of the lowland River Spree and an adjacent oxbow. Groundwater exfiltration was the dominant process, and only fast surface water level rises resulted in temporary infiltration into the aquifer. The main groundwater flow paths are identified based on a 3D groundwater flow model. To estimate mass fluxes across the aquifer–surface water interfaces, a 2D flow and heat transport modelling approach along a transect of 12 piezometers was performed. Results of steady‐state and transient water level simulations show an overall high accuracy with a Spearman coefficient ρ = 0.9996 and root mean square error (RMSE) = 0.008 m. Based on small groundwater flow velocities of about 10^?7 to 10^?6 ms^?1, mean groundwater exfiltration rates of 233 l m^?2 d^?1 are calculated. Short periods of surface water infiltration into the aquifer do not exceed 10 days, and the infiltration rates are in the same range. The heat transport was modelled with slightly less accuracy (ρ = 0.8359 and RMSE = 0.34 °C). In contrast to the predominant groundwater exfiltration, surface water temperatures determine the calculated temperatures in the upper aquifer below both surface water bodies down to 10 m during the whole simulation period. These findings emphasize prevailing of heat conduction over advection in the upper aquifer zones, which seems to be typical for lowland streams with sandy aquifer materials and low hydraulic gradients. Moreover, this study shows the potential of coupled numerical flow and heat transport modelling to understand groundwater–surface water exchange processes in detail. Copyright © 2013 John Wiley & Sons, Ltd.     

Water temperature modelling in a controlled environment: comparative study of heat budget equations

One of the challenges when modelling a complex variable such as water temperature in rivers is that it can be difficult to determine the sources of error and to ensure that the simulations are truly representative of the reality. Therefore, a heat budget study was completed in a controlled environment, which excluded advection and bottom fluxes but enabled observation of all the other fluxes. A 21.42 m³ pool was installed and insulated to limit heat exchange through the sides and bottom. All the major energy fluxes were monitored for a 50‐day period. Different equations for individual heat budget terms were tested to determine their ability to reproduce the observations. This experiment also permitted to assess the relative importance of each component of the heat budget. Performance of each semi‐empirical equation was determined by comparing predictions and measured values. It was thus possible to choose the formulae that best represented the measured heat exchange processes, while understanding the limits of some of the semi‐empirical representations of heat exchange processes. The results highlight the importance of radiative terms into the heat budget because they controlled the major sources and sinks. The study also showed the importance of the wind function determination into the calculation of latent heat flux. The resulting water temperature model returned simulated hourly water temperature with an overall root mean square error of 0.71 °C/h and a modified Nash–Sutcliffe coefficient of 0.97. Copyright © 2012 John Wiley & Sons, Ltd.     

The effects of climatic variability on estimates of recharge from temperature profiles

Using heat as a tracer allows for estimation of ground water recharge rates based on subsurface temperature measurements. While possible in theory, it may be difficult in practice to discriminate the effects of climate from the effects of ground water advection. This study uses synthetic simulations to determine the influence of variability of ground surface temperature (GST) on the ability to estimate vertical specific discharge from temperature profiles. Results suggest that in cases where temperature measurements are sufficiently deep and specific discharge is sufficiently high, estimates of specific discharges will be reasonably accurate. Increasing the number of times temperatures are measured, or producing models that incorporate variations in GST, will increase the reliability of any studies using temperatures to estimate specific discharge. Furthermore, inversions of temperature measurements should be combined with other methods of estimating recharge rates to improve the reliability of recharge estimates.     

Analytical solutions for benchmarking cold regions subsurface water flow and energy transport models: One-dimensional soil thaw with conduction and advection

Numerous cold regions water flow and energy transport models have emerged in recent years. Dissimilarities often exist in their mathematical formulations and/or numerical solution techniques, but few analytical solutions exist for benchmarking flow and energy transport models that include pore water phase change. This paper presents a detailed derivation of the Lunardini solution, an approximate analytical solution for predicting soil thawing subject to conduction, advection, and phase change. Fifteen thawing scenarios are examined by considering differences in porosity, surface temperature, Darcy velocity, and initial temperature. The accuracy of the Lunardini solution is shown to be proportional to the Stefan number. The analytical solution results obtained for soil thawing scenarios with water flow and advection are compared to those obtained from the finite element model SUTRA. Three problems, two involving the Lunardini solution and one involving the classic Neumann solution, are recommended as standard benchmarks for future model development and testing.     

Analytical models of steady-state plumes undergoing sequential first-order degradation

An exact, closed‐form analytical solution is derived for one‐dimensional (1D), coupled, steady‐state advection‐dispersion equations with sequential first‐order degradation of three dissolved species in groundwater. Dimensionless and mathematical analyses are used to examine the sensitivity of longitudinal dispersivity in the parent and daughter analytical solutions. The results indicate that the relative error decreases to less than 15% for the 1D advection‐dominated and advection‐dispersion analytical solutions of the parent and daughter when the Damköhler number of the parent decreases to less than 1 (slow degradation rate) and the Peclet number increases to greater than 6 (advection‐dominated). To estimate first‐order daughter product rate constants in advection‐dominated zones, 1D, two‐dimensional (2D), and three‐dimensional (3D) steady‐state analytical solutions with zero longitudinal dispersivity are also derived for three first‐order sequentially degrading compounds. The closed form of these exact analytical solutions has the advantage of having (1) no numerical integration or evaluation of complex‐valued error function arguments, (2) computational efficiency compared to problems with long times to reach steady state, and (3) minimal effort for incorporation into spreadsheets. These multispecies analytical solutions indicate that BIOCHLOR produces accurate results for 1D steady‐state, applications with longitudinal dispersion. Although BIOCHLOR is inaccurate in multidimensional applications with longitudinal dispersion, these multidimensional multispecies analytical solutions indicate that BIOCHLOR produces accurate steady‐state results when the longitudinal dispersion is zero. As an application, the 1D advection‐dominated analytical solution is applied to estimate field‐scale rate constants of 0.81, 0.74, and 0.69/year for trichloroethene, cis‐1,2‐dichloroethene, and vinyl chloride, respectively, at the Harris Palm Bay, FL, CERCLA site.     

Long‐wave radiation and heat flux estimates within a small tributary in Catamaran Brook (New Brunswick,Canada)

River water temperature is an important water quality parameter that also influences most aquatic life. Physical processes influencing water temperature in rivers are highly complex. This is especially true for the estimation of river heat exchange processes that are highly dependent on good estimates of radiation fluxes. Furthermore, very few studies were found within the stream temperature dynamic literature where the different radiation components have been measured and compared at the stream level (at microclimate conditions). Therefore, this study presents results on hydrometeorological conditions for a small tributary within Catamaran Brook (part of the Miramichi River system, New Brunswick, Canada) with the following specific objectives: (1) to compare between stream microclimate and remote meteorological conditions, (2) to compare measured long‐wave radiation data with those calculated from an analytical model, and (3), to calculate the corresponding river heat fluxes. The most salient findings of this study are (1) solar radiation and wind speed are parameters that are highly site specific within the river environment and play an important role in the estimation of river heat fluxes; (2) the incoming, outgoing, and net long‐wave radiation within the stream environment (under the forest canopy) can be effectively calculated using empirical formula; (3) at the study site more than 80% of the incoming long‐wave radiation was coming from the forest; (4) total energy gains were dominated by solar radiation flux (for all the study periods) followed by the net long‐wave radiation (during some periods) whereas energy losses were coming from both the net long‐wave radiation and evaporation. Conductive heat fluxes have a minor contribution from the overall heat budget (<3·5%); (5) the reflected short‐wave radiation at the water surface was calculated on average as 3·2%, which is consistent with literature values. Results of this study contribute towards a better understanding of river heat fluxes and water temperature models as well as for more effective aquatic resources and fisheries management. Copyright © 2011 John Wiley & Sons, Ltd.     

Study of stream temperature dynamics and corresponding heat fluxes within Miramichi River catchments (New Brunswick,Canada)

Water temperature is a key physical habitat determinant in lotic ecosystems as it influences many physical, chemical, and biological properties of rivers. Hence, a good understanding of the thermal regime of rivers and river heat fluxes is essential for effective management of water and fisheries resources. This study dealt with the modelling of river water temperature using a deterministic model. This model calculated the different heat fluxes at the water surface and from the streambed using different hydrometeorological conditions. The water temperature model was applied on two watercourses of different sizes and thermal characteristics, but within a similar meteorological region, namely, the Little Southwest Miramichi River and Catamaran Brook (New Brunswick, Canada). The model was also applied using microclimate data, i.e. meteorological conditions within the river environment (1–2 m above the water surface), for a better estimation of river heat fluxes. Water temperatures at different depths within the riverbed were also used to estimate the streambed heat fluxes. Results showed that microclimate data were essential to get accurate estimates of the surface heat fluxes. Results also showed that for larger river systems, the surface heat fluxes were generally the dominant component of the heat budget with a correspondingly smaller contribution from the streambed. As watercourses became smaller and groundwater contribution more significant, the streambed contribution became important. For instance, approximately 80% of the heat fluxes occurred at the surface for Catamaran Brook (20% from the streambed) whereas the Little Southwest Miramichi River showed values closer to 90% (10% from the streambed). As was reported in previous studies, the solar radiation input dominated the contribution to the heat gain at 63% for Catamaran Brook and 89% for Little Southwest Miramichi River. Copyright © 2011 John Wiley & Sons, Ltd.     

A numerical model for estimating groundwater flux from subsurface temperature profiles

A simple numerical model is presented for estimating vertical groundwater flux from transient subsurface temperature profiles obtained from field measurements. The model developed utilizes the MacCormack scheme, which is based on the Finite Difference Method (FDM), for solving the governing partial differential equation of convection–diffusion heat transport with appropriate initial and boundary conditions within the subsurface. In order to validate the model, numerical solutions obtained for the study area located in the Nagoka plain, Japan are compared with the published measured data and results obtained by others. Results obtained show good agreement and fit the observed data with a correlation coefficient, R², of 0·88. The estimated groundwater flux is 1·85 × 10⁻⁷ m s⁻¹. Sensitivity analyses were also carried out to investigate the effect of variations in groundwater fluxes, thermal properties and the annual thermal variability due to climatic changes on the transient subsurface temperature profiles and to have a better understanding of the subsurface thermal dynamics. A substantial effect of annual climatic variability is observed on the temporal distributions of temperature depth profiles, and a better estimate of thermal parameters is required to estimate vertical groundwater flux. The largest change in subsurface temperature depth profiles due to groundwater flux over a year is within ± 4 °C. The influence of groundwater flux on subsurface temperature distributions in space and time may be more pronounced in areas where the top of the saturated layer fluctuates considerably. Variation in thermal diffusivity results in temperature change up to ± 1·5% and may cause change in groundwater flux estimate by ± 18%. The model presented has merits over analytical solutions (type curve matching techniques) in terms of suitability and applicability to real field problems, and can be a good asset to hydrological models as quantifying groundwater recharge or deducing it from other quantities, such as rainfall, evapotranspiration and runoff, is often complicated. Copyright © 2007 John Wiley & Sons, Ltd.     

Estimation of vertical water and heat fluxes in the semi-confined aquifers in tokyo metropolitan area,japan

Groundwater circulation is known to be one of the agents responsible for the redistribution of geothermal energy by acting as a source or sink in the course of its movement through porous media. Heat transport in groundwater systems is considered to be a coupled process and the theory based on this was used to analyse temperature profiles of 30 thermally stable observation wells in a deep, semi-confined aquifer system in the Tokyo Metropolitan area. Vertical water fluxes in the semi-confined aquifers and the associated upward heat fluxes were estimated from a heat flux equation that describes convection and conduction processes of heat transport in one dimension. The vertical downward water fluxes in Shitamachi lowland, Musashino and Tachikawa terraces were 0.69.26.91 × 10^?9, 1.46-70.92 × 10^?9 and 2.61.2204 × 10^?9 m/s, respectively. A vertical upward water flux of 1.80-33.60 × 10^?9 m/s was estimated in Shitamachi lowland. The water flux generally decreased with increasing depth for observation wells which intercepted more than one semi-confining layer. The estimated upward heat fluxes for Shitamachi lowland, Musashino and Tachikawa terraces were 0.32-1.12, 0.49-1.21 and 1.00-11.62 W/m², respectively. The heat flux was highest in Tachikawa terrace where a major fault, the Tachikawa fault, is located. Generally, the estimated heat flux was higher in the semi-confining layers than in the aquifers. Areas with heat sources and sinks as well as groundwater flow patterns in the semi-confined aquifers were revealed by heat flux and temperature distributions in the study area.     

From streambed temperature measurements to spatial‐temporal flux quantification: using the LPML method to study groundwater–surface water interaction

Knowledge on groundwater–surface water interaction and especially on exchange fluxes between streams and aquifers is an important prerequisite for the study of transport and fate of contaminants and nutrients in the hyporheic zone. One possibility to quantify groundwater–surface water exchange fluxes is by using heat as an environmlental tracer. Modern field equipment including multilevel temperature sticks and the novel open‐source analysis tool LPML make this technique ever more attractive. The recently developed LPML method solves the one‐dimensional fluid flow and heat transport equation by combining a local polynomial method with a maximum likelihood estimator. In this study, we apply the LPML method on field data to quantify the spatial and temporal variability of vertical fluxes and their uncertainties from temperature–time series measured in a Belgian lowland stream. Over several months, temperature data were collected with multilevel temperature sticks at the streambed top and at six depths for a small stream section. Long‐term estimates show a range from gaining fluxes of ?291 mm day^?1 to loosing fluxes of 12 mm day^?1; average seasonal fluxes ranged from ?138 mm day^?1 in winter to ?16 mm day^?1 in summer. With our analyses, we could determine a high spatial and temporal variability of vertical exchange fluxes for the investigated stream section. Such spatial and temporal variability should be taken into account in biogeochemical cycling of carbon, nutrients and metals and in fate analysis of contaminant plumes. In general, the stream section was gaining during most of the observation period. Two short‐term high stream stage events, seemingly caused by blockage of the stream outlet, led to a change in flow direction from gaining to losing conditions. We also found more discharge occurring at the outer stream bank than at the inner one indicating a local flow‐through system. With the conducted analyses, we were able to advance our understanding of the regional groundwater flow system. Copyright © 2015 John Wiley & Sons, Ltd.     

Impact of heat advection on the thermal regime of roads built on permafrost

In northern regions, transportation infrastructure can experience severe structural damages due to permafrost degradation. Water infiltration and subsurface water flow under an embankment affect the energy balance of roadways and underlying permafrost. However, the quantification of the processes controlling these changes and a detailed investigation of their thermal impacts remain largely unknown due to a lack of available long-term embankment temperature data in permafrost regions. Here, we report observations of heat advection linked to surface water infiltration and subsurface flow based on a 9-year (from 2009 to 2017) thermal monitoring at an experimental road test site built on ice-rich permafrost conditions in southwestern Yukon, Canada. Our results show that snowmelt water infiltration in the spring rapidly increases temperature in the upper portion of the embankment. The earlier disappearance of snow deposited at the embankment slope increases the thawing period and the temperature gradient in the embankment compared with the natural ground. Infiltrated summer rainfall water lowered the near-surface temperatures and subsequently warmed embankment fill materials down to 3.6-m depth. Heat advection caused by the flow of subsurface water produced warming rates at depth in the embankment subgrade up to two orders of magnitude faster than by atmospheric warming (heat conduction). Subsurface water flow promoted permafrost thawing under the road embankment and led to an increase in active layer thickness. We conclude that the thermal stability of roadways along the Alaska Highway corridor is not maintainable in situations where water is flowing under the infrastructure unless mitigation techniques are used. Severe structural damages to the highway embankment are expected to occur in the next decade.     

Spatio‐temporal variability of water and energy fluxes – a case study for a mesoscale catchment in pre‐alpine environment

Water and energy fluxes at and between the land surface, the subsurface and the atmosphere are inextricably linked over all spatio‐temporal scales. Our research focuses on the joint analysis of both water and energy fluxes in a pre‐alpine catchment (55 km²) in southern Germany, which is part of the Terrestrial Environmental Observatories (TERENO). We use a novel three‐dimensional, physically based and distributed modelling approach to reproduce both observed streamflow as an integral measure for water fluxes and heat flux and soil temperature measurements at an observation location over a period of 2 years. While heat fluxes are often used for comparison of the simulations of one‐dimensional land surface models, they are rarely used for additional validation of physically based and distributed hydrological modelling approaches. The spatio‐temporal variability of the water and energy balance components and their partitioning for dominant land use types of the study region are investigated. The model shows good performance for simulating daily streamflow (Nash–Sutcliffe efficiency > 0.75). Albeit only streamflow measurements are used for calibration, the simulations of hourly heat fluxes and soil temperatures at the observation site also show a good performance, particularly during summer. A limitation of the model is the simulation of temperature‐driven heat fluxes during winter, when the soil is covered by snow. An analysis of the simulated spatial fields reveals heat flux patterns that reflect the distribution of the land use and soil types of the catchment. The water and energy partitioning is characterized by a strong seasonal cycle and shows clear differences between the selected land use types. Copyright © 2016 The Authors Hydrological Processes Published by John Wiley & Sons Ltd.     

Some thermal and mechanical consequences of rapid uplift: an example from the Southern Alps, New Zealand

The thermal evolution of continental crust during active collision is modeled through numerical solutions of the two-dimensional heat conduction equation for a rapidly moving medium. The boundary conditions used in the modeling are derived from geological and geophysical observations from the active collision zone in the South Island of New Zealand. The problem domain over which the solutions are obtained consists of a 40 km horizontal by 25 km vertical spatial plane with a vertical discontinuity at 10 km from the western boundary. To the east of this discontinuity, vertical uplift rates of up to 10 mm/a occur over a timespan of up to 4 Ma. Temperature distributions are calculated at 10 ka intervals over the 4 Ma duration. A two-dimensional high-temperature region is established upon initiation of uplift of the eastern block due to the advective component carrying heat upwards more rapidly than it can be dissipated laterally from the problem domain. Temperatures within the upper 5 km are greater than 400°C after 2.25 Ma with geothermal gradients of up to 200°C/km attained within the upper 3 km. At times greater than 2.5 Ma, the vertical temperature distribution changes little while the anomalously high temperatures spread laterally into the stationary crust.Using rheological equations to describe the brittle behaviour of a water-saturated upper crust and the ductile behaviour of a quartz-dominated lower crust, together with the thermal distribution of the conduction models, the mechanical evolution of a collision zone is investigated. In addition to high crustal temperatures and associated high heat flow, rapid uplift produces a weakening of the crust by raising of the depth of transition from brittle to ductile behaviour. Within the zone of most rapid uplift, the brittle-ductile transition rises from 13 km to less than 5 km after 1.5 Ma of uplift. Further uplift reduces the brittle layer to 3 km thickness and causes lateral spreading of the low-strength zone. The reductions in crustal strength caused by the thermal weakening produce a high-strain zone within the region of maximum uplift which is incapable of sustaining large differential stresses. This causes horizontal and vertical stress transfer and results in shallow seismicity increases in the adjacent crust as well as in intermediate depth seismicity within the high-strength upper mantle.Because the thermal and mechanical anomalies discussed are a function of rapid uplift, all regions of active continental collision may be expected to exhibit similar behaviour. Some mechanical and thermal characteristics of the Himalayan collision zone are briefly examined in light of the numerical modeling.     

Modelling in‐pool temperature variability in a beaded arctic stream

This study examines the variability of in‐pool temperatures in Imnavait Creek, a beaded arctic stream consisting of small pools connected by shallow chutes, for the purpose of predicting potential impacts of climate variations on the system. To better understand heat fate and transport through this system, the dominant heat sources and sinks creating and influencing thermal stratification within even the smallest and shallowest pools must be quantified. To do this, temperature data were collected vertically within the pool water column and surrounding bed sediments during stratified conditions. These temperature and other supporting data (e.g. instream flow, weather data, and bathymetry) were used to formulate and develop an instream temperature model that captures the site‐specific processes occurring within the pools during summer low flow conditions. The model includes advective, air–water interface, and bed conduction fluxes, simplified vertical exchange between stratified pool layers, and attenuation of shortwave radiation within the water column. We present the model formulation, data collection methods used in support of model development and population, and the resulting model calibration and validation for one of the study pools. We also provide information regarding dominant heat sources and sinks and residence times of different layers within the stratified pool. We found that the dominant heat sources vary between stratified layers and that increases in thaw depths surrounding these pools due to possible climate changes can shift stratification, mixing, and instream storage dynamics, thereby influencing the fate and transport of heat and other constituents of interest (e.g. nutrients). Copyright © 2011 John Wiley & Sons, Ltd.     

热带对流热量与水汽收支的数值模拟研究

应用二维云分辨模式,数值研究了热带地区的对流活动,并诊断了热量和水汽的收支,发现在垂直温度平流和凝结潜热释放之间、垂直水汽平流和降水之间都维持着大体平衡,推断出质量加权平均温度及可降水分的局地变化分别由热量及水汽方程中的剩余项决定.机制研究表明,深对流与浅对流在热量及水汽循环中存在较大差异,深对流中水汽的凝结及潜热释放起着主导作用,而大尺度垂直平流的加湿和冷却在浅对流中发挥主导作用.最后讨论了对流触发后热量及水汽循环的调整机制.