Vertical Heat Transport Research Articles

Dual‐scale transport of sensible heat and water vapor over a short canopy under unstable conditions

This study examines the nature of vertical transport of sensible heat and water vapor density due to mesoscale motions and how they are observed with surface eddy covariance systems. For this purpose, turbulence data measured above a flat and irrigated rice paddy field under unstable conditions were analyzed. It was shown that the larger‐scale component in the measured time series represents mesoscale motions. Wavelet cospectra of the scalar fluxes revealed the presence of vertical transport at horizontal scales larger than the cospectral gap. A time series and the eddy covariance flux were decomposed into a turbulence and a mesoscale component using the identified cospectral gap. The mesoscale transport component of sensible heat and water vapor were found to be related to the wind direction and therefore characteristic of the upwind surface conditions at this scale. In contrast, the turbulence flux component exhibits universal attributes resulting from the local surface characteristics.

Speculations on the Thermal and Tectonic History of the Earth

The connection between the Earth's thermal history and convection in the mantle is exploited to elucidate the early evolution of the Earth. It appears probable that convection extending over almost all of the mantle has dominated vertical heat transport throughout the whole of the Earth's history. Only in boundary layers at the surface and at a depth of 650–700 km is conduction likely to be important. The resulting evolution appears to be consistent with geological observations on early Precambrian rocks. Various arguments are put forward in favour of two horizontal scales of convective flow in the mantle at depths less than 650 km. The large scale flow is related to the motion of major plates, and must be ordered over distances of more than 5000 km. Its evolution and energetics are discussed and there are no obvious problems in maintaining the proposed convective motions. Small scale flow with an extent of the order of 500 km appears necessary both to explain the heat flow through older parts of the Earth's surface and to reconcile the geophysical observations with the results of numerical experiments. Though the existence of the small scale flow is at present speculative, various tests of its presence are proposed.

Modelling sensible and latent heat fluxes over sea during unstable, very close to neutral conditions

During slightly unstable but still very close to neutral conditions new results from two previous investigations have shown a significant increase of sensible and latent heat fluxes over the sea. The vertical heat transport during these conditions is dominated by detached eddies originating at the top of the boundary layer, bringing relatively cold and dry air to the surface. This effect can be described in numerical models by either enhanced heat transfer coefficients for sensible and latent heat (Stanton and Dalton numbers respectively) or with an additional roughness length, added to the original roughness lengths for heat and humidity. Such new expressions are developed using turbulence measurements from the Baltic Sea valid for wind speeds up to 14 m s−1. The effect of including the increased heat fluxes is investigated using two different numerical models: a regional three-dimensional climate model covering northern Europe, and a process-oriented ocean model for the Baltic Sea. During periods of several days, the latent heat flux can be increased by as much as 100 W m−2. The increase in sensible heat flux is significantly smaller since the process is only of importance in the very near-neutral regime where the sensible heat flux is very small. The long-term average effect over the Baltic Sea is of the order of several W m−2.

Environmental implications of stratification and turbulent mixing in a shallow lake basin

The extent of stratification and vertical mixing in the water column (7–11 m deep) was investigated over an offshore reef in the western basin of Lake Erie. Measurements reveal that the vertical transport of oxygen and heat is controlled by the complex interaction of several physical mechanisms. Generally, when the wind speed (W) was >7 m·s–1 and the air was cooler than the water (Tair< Tw), the water column was well mixed due to turbulent mixing. However, when W < 7 m·s–1 (~65% of the summer), turbulence was too weak to overcome the stratification and mix the water column. An analysis of 25 years of meteorological data revealed that a period of 4.5 ± 1.9 days of calm, warm weather (W < 7 m·s–1 and Tair > Tw) occurs every year. Results indicate that there is strong probability of hypoxia due to stratification (i.e., when diffusivities < 10–6 m2·s–1) and sediment oxygen demand (i.e., 0.1–1.0 g·m–2·day–1) during these periods. The environmental implications of stratification to water quality and its effects on benthic organisms, such as the burrowing mayfly (Hexagenia spp.), require further considerations in large temperate lakes and basins that are sufficiently shallow that there is no permanent seasonal stratification.

Heat transport in the Red Lake Bog, Glacial Lake Agassiz Peatlands

AbstractWe report the results of an investigation on the processes controlling heat transport in peat under a large bog in the Glacial Lake Agassiz Peatlands. For 2 years, starting in July 1998, we recorded temperature at 12 depth intervals from 0 to 400 cm within a vertical peat profile at the crest of the bog at sub‐daily intervals. We also recorded air temperature 1 m above the peat surface. We calculate a peat thermal conductivity of 0·5 W m−1 °C−1 and model vertical heat transport through the peat using the SUTRA model. The model was calibrated to the first year of data, and then evaluated against the second year of collected heat data. The model results suggest that advective pore‐water flow is not necessary to transport heat within the peat profile and most of the heat is transferred by thermal conduction alone in these waterlogged soils. In the spring season, a zero‐curtain effect controls the transport of heat through shallow depths of the peat. Changes in local climate and the resulting changes in thermal transport still may cause non‐linear feedbacks in methane emissions related to the generation of methane deeper within the peat profile as regional temperatures increase. Copyright © 2006 John Wiley & Sons, Ltd.

Heat flux intensification by vortical flow localization in rotating convection

The effect of rotation on turbulent convective flow between parallel plates has been assessed with direct numerical simulations. With increasing rotation-rate an interesting transition is observed in the vertical-velocity skewness. This transition indicates a localization of motion directed away from the wall and correlates well with changes observed in the heat flux, as well as in the thermal and viscous boundary layer thicknesses. The formation of localized intense vortical structures provides for intensified vertical heat transport through Ekman pumping. At higher rotation-rates this is counteracted by the inhibition of vertical motion by rotation as expressed in the geostrophic thermal-wind balance.

Turbulent fluxes from Helipod flights above quasi-homogeneous patches within the LITFASS area

Turbulent fluxes of sensible and latent heat were measured with the helicopter-borne turbulence probe Helipod over a heterogeneous landscape around the Meteorological Observatory Lindenberg during the STINHO-2 and LITFASS-2003 field experiments. Besides the determination of area-averaged heat fluxes, the analysis focused on different aspects of the response of the turbulent structure of the convective boundary layer (CBL) on the surface heterogeneity. A special flight pattern was designed to study flux profiles both over quasi-homogeneous sub-areas of the study region (representing the major land use types—forest, farmland, water) and over a typical mixture of the different surfaces. Significant differences were found between the heat fluxes over the individual surfaces along flight legs at about 80 m above ground level, in agreement with large-aperture scintillometer measurements. This flux separation was still present during some flights at levels near the middle of the CBL. Different scales for the blending height and horizontal heterogeneity were calculated, but none of them could be identified as a reliable indicator of the mixing state of the lower CBL. With the exception of the flights over water, the latent heat flux measurements generally showed a larger statistical error when compared with the sensible heat flux. Correlation coefficients a nd integral length scales were used to characterise the interplay between the vertical transport of sensible and latent heat, which was found to vary between ‘fairly correlated’ and ‘decoupled’, also depending on the soil moisture conditions.

Thermobaric deep convection, baroclinic instability, and their roles in vertical heat transport around Maud Rise in the Weddell Sea

Numerical experiments with two‐ and three‐dimensional nonhydrostatic models in a rotating frame have been executed to investigate thermobaric deep convection, subsequent baroclinic instability, and their roles in vertical heat transport, using hydrographic data around Maud Rise in the Weddell Sea, Antarctica. Overturning of the water column due to thermobaric convection is apt to occur on the southern and northern flanks of the rise, and induces upward heat transport. The depth of overturning is two times larger on the northern flank (∼1.5 km) than on the southern flank (∼0.7 km). To the contrary, no overturning occurs over the top of the rise in 90 days. Baroclinic instability develops at a density front formed between the overturned and unoverturned regions since a density contrast at the front is enhanced by thermobaricity. Heat transport due to baroclinic instability is similarly upward, and at peak becomes comparable to that due to the overturning. Applicability of the results to the cooling events previously reported is also discussed.

Bounds on vertical heat transport for infinite-Prandtl-number Rayleigh–Bénard convection

For the infinite-Prandtl-number limit of the Boussinesq equations, the enhancement of vertical heat transport in Rayleigh-Benard convection, the Nusselt number Nu, is bounded above in terms of the Rayleigh number Ra according to Nu≤0.644× Ra 1/3 [log R a ] 1/3 as R a → ∞. This result follows from the utilization of a novel logarithmic profile in the background method for producing bounds on bulk transport, together with new estimates for the bi-Laplacian in a weighted L 2 space. It is a quantitative improvement of the best currently available analytic result, and it comes within the logarithmic factor of the pure 1/3 scaling anticipated by both the classical marginally stable boundary layer argument and the most recent high-resolution numerical computations of the optimal bound on Nu using the background method.

The impact of crop growth sub-model choice on simulated water and nitrogen balances

It is the aim of this study to analyse how different crop growth model routines affect the simulation of water flow and nitrogen transport of a crop rotation in agricultural fields. The model system Expert-N is briefly described and used to test the crop growth sub-models against data of a six-year field experiment on sandy soils. Expert-N is a modular soil–plant–atmosphere model system, which comprises different sub-models to simulate one-dimensional vertical transport of water, solute and heat in the unsaturated zone. It includes several sub-models to describe organic matter turnover and has three generic crop growth sub-models. The latter are derived from the crop models CERES, SPASS and SUCROS. Simulations were performed using the different sub-models for each of the cereal crops in the sugar beet, winter wheat, winter barley, winter rye crop rotation. Results show the impact of crop model choice on simulated water balances and turnover of C and N. It is concluded that the simulation of root growth and plant residue mineralisation needs some improvement.

Impact‐induced hydrothermal activity on early Mars

We report on numerical modeling results of postimpact cooling of craters with diameters of 30, 100, and 180 km in an early Martian environment, with and without the presence of water. The effects of several variables, such as ground permeability and the presence of a crater lake, were tested. Host rock permeability is the main factor affecting fluid circulation and lifetimes of hydrothermal systems, and several permeability cases were examined for each crater. The absence of a crater lake decreases the amount of circulating water and increases the system lifetime; however, it does not dramatically change the character of the system as long as the ground remains saturated. It was noted that vertical heat transport by water increases the temperature of localized near‐surface regions and can prolong system lifetime, which is defined by maximum near‐surface temperature. However, for very high permeabilities this effect is negated by the overall rapid cooling of the system. System lifetimes, which are defined by near‐surface temperatures and averaged for all permeability cases examined, were 67,000 years for the 30‐km crater, 290,000 years for the 100‐km crater, and 380,000 for the 180‐km crater. Also, an approximation of the thermal evolution of a Hellas‐sized basin suggests potential for hydrothermal activity for ∼10 Myr after the impact. These lifetimes provide ample time for colonization of impact‐induced hydrothermal systems by thermophilic organisms, provided they existed on early Mars. The habitable volume reaches a maximum of 6,000 km38,500 years after the impact in the 180‐km crater model.

A simple convective model of the global overturning circulation, including effects of entrainment into sinking regions

We use a simple conceptual model to examine the roles of vertical mixing and surface buoyancy fluxes in the dynamics of the global overturning circulation that ventilates the deep oceans. In addition to using the Munk [Munk, W.H., 1966. Abyssal recipes. Deep-Sea Research 13, 707–730] advection–diffusion balance in the ocean interior, we close the circulation by including the small high-latitude sinking regions, which are assumed to be turbulent geostrophic gravity currents on gentle topographic slopes. The interior and sinking regions are coupled by turbulent entrainment into the sinking regions and we examine the global influence of this entrainment. An important realization is that the rates of mixing into slope currents, predicted to be very small as a function of along-flow distance, imply rates of entrainment per unit depth of fall that are comparable to the entrainment rate for vertical plumes. The overturning mass flux and ocean density stratification are found as a function of the vertical diffusivity and total heat transport. Given a realistic heat transport and the measured average mixing rate of order 10 −5 m 2/s, this simple model yields predictions consistent with data for the increase in volume flux with depth in slope currents, the magnitude of the global overturning circulation, and the averaged top-to-bottom density difference. Despite the absence of other mechanisms thought to be important in the thermocline, the model also gives a realistic thermal boundary layer thickness. As a consequence of entrainment into the dense sinking currents, the linking of abyssal densities to surface fluxes and the assumption of a uniform diffusivity, the model convective flow requires much less energy than the Munk (1966) prediction. The results indicate that the ocean overturning is feasibly a convective one and we suggest there might be no need to search for ‘missing’ mixing.

Numerical study of baroclinic instability associated with thermobaric deep convection at high latitudes: Idealized cases

Numerical experiments with a three-dimensional nonhydrostatic model in a rotating frame have been executed to investigate baroclinic instability associated with thermobaric deep convection in weakly stratified polar oceans and its role in the transport processes. The model ocean has a two-layered structure with the cold, fresh mixed layer overlying the warm, saline deep water cell, as in the Weddell Sea. In contrast with a scenario based on the linear equation of state, thermobaric overturning of the water column enhances the horizontal density gradient (baroclinicity) through nonlinearity of the equation of state. If temperature controls water density (TEM cases), baroclinicity is intensified at the bottom of the overturned layer while at the surface if salinity does (SAL cases). Such intensification causes further development of baroclinic instability or baroclinic destabilization and more effective vertical heat transport. In the post-overturning stage, on the other hand, surface cooling (convective motion) has two oppositely operating effects on baroclinic instability and the associated heat transport. One is that horizontal convergence due to convective motion enhances baroclinic instability in the surface layer, as in previous studies focusing on strongly stratified oceans. This is observed in SAL cases with weak cooling, but not in TEM cases. The other is that strong cooling suppresses baroclinic instability by homogenizing the overturned layer vertically. This effect has not been found in the strongly stratified oceans. As a result, the vertical heat transport is most effective at low cooling rates ( ∼ 125 W m - 2 ) in SAL cases while it monotonically decreases with cooling rate in TEM cases. When baroclinicity is initially weak as in the Weddell Sea, the most effective transport occurs with the cooling rate of 25 W m - 2 which is a possible value under sea-ice cover in the actual situation.

Vertical heat and constituent transport in the mesopause region by dissipating gravity waves at Maui, Hawaii (20.7°N), and Starfire Optical Range, New Mexico (35°N)

Vertical heat flux profiles induced by dissipating gravity waves in the mesopause region (85–100 km altitude) are derived from Na lidar measurements of winds and temperatures at Maui (20.7°N, 156.3°W), Hawaii, and compared with earlier results from Starfire Optical Range (SOR, 35.0°N, 106.5°W), New Mexico. The heat flux profile at SOR has a single downward maximum of 2.25 ± 0.3 K m/s at 88 km, while the profile at Maui has two downward maxima of 1.25 ± 0.5 K m/s and 1.40 ± 0.5 K m/s at 87 and 95 km, respectively. The common maximum below 90 km can be attributed to high probability of convective instability. Comparison of the horizontal wind shear suggests that the second maximum at 95 km at Maui may be associated with dynamic instability. The measured Na flux and predicted Na flux based on measured heat flux at Maui agree well, further confirming earlier findings using SOR data. The dynamical flux of atomic oxygen estimated from the heat flux is smaller at Maui compared with that at SOR, but both are comparable to or larger than the eddy flux. The results also suggest that weaker gravity wave dissipation at Maui may cause two opposite effects on the energy balance in the mesopause region, a reduced cooling from heat transport and reduced chemical heating from atomic oxygen transport.

Infrared observations and numerical modelling of grassland fires in the Northern Territory, Australia

This paper reports on a small-scale pilot experiment held early in the dry season near Darwin, Australia, in which fine-scale observations of several prescribed fires were made using infrared digital video. Infrared imaging is used routinely to locate fires as infrared radiation suffers little attenuation as it propagates through the smoke that normally obscures visible imagery. However, until now, little use has been made of digital video imagery in analyzing the convective-scale structure of prescribed (or wild) fires. The advantage of digital video imagery is that the individual frames can be objectively analyzed to determine the convective motion in the plane viewed by the camera. The infrared imagery shows mostly rising plumes, much like convective clouds. The flow is highly convective, and the vertical transport of heat is confined to relatively narrow thermals. The updrafts range from a few m s−1 to around 15 m s−1. A numerical model is used to simulate one of the prescribed fires at very high-resolution. For the most part, the model predictions compare well to the observations. The model produces plumes that are around 7 m high, and spaced around 5 m apart, which is similar to that observed. The model correctly predicts the mean rate of spread of the fire to be 1.3 m s−1. Perhaps the most serious limitations to using infrared observations of the type presented here are the difficulties in interpreting precisely the relationship between the observed infrared temperature field and the air temperature calculated by the model, and the exact connection between the infrared camera derived flow field and that calculated by the model.

THE IMPACT OF THE SURFACE HETEROGENEITY ON THE ENERGY IMBALANCE PROBLEM USING LES

Heterogeneous surface conditions modify the flow structure of the convective boundary layer (CBL). We investigated this impact focusing on the spatial representativeness of eddy-covariance (EC) point observations. The typical daytime boundary layer was simulated using large eddy simulation (LES), where horizontal heterogeneity was imposed on the ground surface heating as one-dimensional sinusoidal variation. The effect of variation of the wavelength and amplitude on the vertical heat transport was examined.The surface budged based on the point EC method is examined excluding the net vertical heat transport due to the mesoscale circulations invoked by surface heterogeneity. The mesoscale circulation is represented using a phase average. The result found that our simulated EC point measurements still underestimate this energy budget. However, this deficit gets close to zero when the surface heterogeneity is strong. This underestimate can be strongly attributed to the turbulent organized structure (TOS) developed parallel to the mesoscale circulation.

Evolution mechanisms of the intraseasonal oscillation associated with the Yangtze River Basin flood in 1998

With 1998 NCEP reanalysis data and the linear diagnostic equation for local meridional circulation, four main processes and the boundary effects with relatively large contributions to the intraseasonal oscillation of the vertical branches of the East Asian meridional circulation are quantitatively identified among all the processes involved in the quasi-primitive equations used in the derivation of the linear diagnostic equation. The numerical results show that the main processes with maximal contributions in the lower latitudes include the latent heating and vertical transports of sensible heat. These processes are mainly associated with the tropical convective activities and result in the low-frequency cyclones in the lower latitudes. The main processes with maximal contributions in the higher latitudes are the horizontal transports of westerly momentum and horizontal temperature advections. These processes are mainly associated with the fluctua-tions in the westerlies and result in the low-frequency cyclones in the higher latitudes. The low-frequency cyclones propagating away from lower latitudes not only interact with those from higher latitudes to enhance the lifting of the moist air in the Yangtze River Basin (YRB), but also leave room for the development of the low-frequency anticyclones over the South China Sea (SCS). The southwesterly in the northwestern quadrant of the SCS anticyclones provides the YRB with abundant moisture. This favorable moisture condition along with the enhanced rising motion in the YRB leads to the extraordinary flood in 1998.

Borehole temperatures, climate change and the pre-observational surface air temperature mean: allowance for hydraulic conditions

Joint analysis of surface air temperature series recorded at weather stations together with the inversion of the temperature-depth profiles logged in the near-by boreholes enables an estimate of the conditions existing prior to the beginning of the meteorological observation, the so-called pre-observational mean (POM) temperature. Such analysis is based on the presumption of pure diffusive conditions in the underground. However, in real cases a certain subsurface fluid movement cannot be excluded and the measured temperature logs may contain an advective component. The paper addresses the correction for the hydraulic conditions, which may have perturbed the climate signal penetrating from the surface into the underground. The method accounts for vertical conductive and vertical advective heat transport in a 1-D horizontally layered stratum and provides a simultaneous evaluation of the POM-temperature together with the estimate of the Darcy fluid velocity. The correction strategy is illustrated on a synthetic example and its use is demonstrated on temperature logs measured in four closely spaced boreholes drilled near Tachlovice (located about 15 km SW of Prague, Czech Republic). The results revealed that in a case of moderately advectively affected subsurface conditions (fluid velocities about 10 −9 m/s), the difference between POM-values assessed for a pure conductive approach and for combined vertical conductive/advective approach may amount up to 0.3–0.5 K, the value comparable with the amount usually ascribed to the 20th century climate warming.

Clustering of plumes in turbulent convection.

Turbulent Rayleigh-Bénard convection produces fields of intense updrafts and downdrafts that are responsible for much of the vertical heat transport. These structures, called plumes or thermals, have horizontal scales comparable to the thicknesses of the boundary layers in which they arise. In the three-dimensional numerical simulations reported here, we have observed that convective plumes organize themselves into clusters with horizontal scales that grow with time and reach the width of the computational domain. In this two-scale process, kinetic energy is transferred mainly to low horizontal wave numbers while the sizes of individual plumes remain on the scale of the boundary layer thickness.

Estimations of Mass Fluxes for Cumulus Parameterizations from High-Resolution Spatial Data

Abstract The core of the mass flux formulation, on which the majority of the current cumulus parameterizations are based, is to transport physical variables by the so-called mass flux for individual physical components, such as convective updrafts, downdrafts, and environment. These parameterizations use horizontal means over the subdomains occupied by these physical components to define the mass fluxes and transported variables. However, evaluations of the mass flux formulation against high-resolution spatial data obtained from explicit numerical models reveal that it substantially underestimates vertical transport of heat, moisture, and momentum by deep convection. The present paper proposes an alternative approach, in which the effective values weighted toward extreme values are used both for the mass flux and the transported variable to obtain an accurate estimate of vertical transport. Statistically, the distribution of convective variables is so widely distributed within individual subdomains that t...