Vertical Heat Transport Research Articles

Comparison of the nonlocal transport characteristics of a series of one-dimensional oceanic boundary layer models

Seven one-dimensional oceanic boundary layer models are investigated to assess the possible nonlocal transport characteristics of mass and heat in the upper ocean. The dynamical models have been chosen from the diffusion and bulk types currently in use plus two modifications of the transilient type that have been used extensively for atmospheric work by Stull. The models are forced using wind speed and insolation conditions recorded during a 9-day oceanographic cruise near Bermuda in March 1993 during the decline of the spring bloom. The attenuation of sunlight in the upper ocean is calculated using a full spectral model for downwelling irradiance. The vertical heat transport characteristics are reported and compared. A series of spectral diagnostic tests (Green's function analysis, process spectra, and overall mixing lengths) reveal significant differences in the vertical transport characteristics of the models that are not observed in commonly used diagnostics such as sea surface temperature or mixed layer depth. Age spectra (or modal time since last surface contact) are calculated from Green's functions and reveal how a water mass can be cut off from the surface within a short time period. The large differences in the vertical mixing characteristics of the upper ocean boundary layer models have potential implications on the vertical distributions of short-lived chemical tracers and phytoplankton.

A diagnostic study on the environmental influence of a mesoscale convective system over southern China in Meiyu season

¶During the Post-TAMEX forecast experiment of Taiwan in 1992, a mesoscale convective system (MCS) developed on June 5–6 over southern China. As this system matured, it produced readily apparent cirrus outflow on satellite imageries while the upper level flow also exhibited a diffluent pattern. The purpose of the current study is to examine the possible changes in its environment associated with the development of this MCS. By using 12-h data from 1200 UTC June 5 to 1200 UTC June 6, objective analyses were performed for a 1°×1° latitude/longitude grid using sounding data and a low-pass filter. To facilitate the diagnosis, a band-pass filter was further applied to separate mesoscale features from macroscale ones, while the apparent heat source and apparent moisture sink defined by Yanai et al (1973) were also calculated. Results suggest that the MCS exerted clearly discernable effects on its environment. The latent heat release led to the development of a warm core and mesoscale high-pressure disturbance at upper levels when the system matured. Ageostrophic winds and diffluent flow patterns together with strong anticyclonic vorticity at 200 hPa near the MCS were associated with the mesohigh. After the mature stage, weak cooling occurred above 350 hPa, likely due to radiative emission from the cloud top. However, a mid-level cyclonic vortex, often present in MCSs over the North America, was not apparent here due to weak environmental vorticity and small Coriolis parameter f. The level of maximum divergence was initially located at 500 hPa, but rose to 200 hPa as the MCS matured. In response, the upward motion not only intensified, but the level at which strongest rising occurred also ascended from 700 to 350 hPa. Results from the apparent heat source and moisture sink calculation suggest that this slow ascent of maximum heating was partially due to vertical transport of sensible heat by updrafts. During the MCS’s mature stage, under the stratiform clouds to the west of the strongest convection, a cold mesohigh formed at the surface due to evaporative cooling in downdrafts, and a gust front appeared along the leading edge of the outflow boundary. A trailing mesolow was also observed, likely due to near-adiabatic warming in drier downdrafts since no precipitation was associated with it.

Estimation of the impact of short-term fluctuations in inputs on temporally aggregated outputs of process-oriented models

Process-oriented models driven by highly resolved meteorological inputs and comprising a short internal time step are sometimes used to predict substance fluxes in air, soil and water over fairly long periods of time. To ascertain whether regression-based input–output analyses in such cases can provide adequate parametric models of the impact of daily and monthly fluctuations in inputs on annual outputs, we studied the SOIL/SOILN model of vertical transport of heat, water and nitrogen through arable soils. Annual leaching of nitrate from the root zone was regarded as the response variable, and regressors were selected from among the set of all linear combinations of daily or monthly values of five different meteorological inputs. We found that, although several of the underlying processes described by the SOIL/SOILN model are non-linear, both ordinary and partial least squares regression (OLS and PLS) identified the subsets of input variables with the strongest influence on the model output, and the dominating time lags between model inputs and outputs. Furthermore, highly resolved explanatory variables were a prerequisite for good performance of linear predictors of temporally aggregated outputs and, to discern the full dynamic behaviour of the model, it was necessary to analyse the response to artificially generated daily meteorological data representing a very large number of different weather conditions. PLS had one advantage over OLS: a smooth pattern in the regression coefficients facilitated physical interpretation of the derived impulse–response weights.

A study on the structure of the convective atmosphere over the Bay of Bengal during BOBMEX-99

Convective activity is one of the major processes in the atmosphere influencing the local and large-scale weather in the tropics. The latent heat released by the cumulus cloud is known to drive monsoon circulation, which on the other hand supplies the moisture that maintains the cumulus clouds. An investigation is carried out on the convective structure of the atmosphere during active and suppressed periods of convection using data sets obtained from the Bay of Bengal and Monsoon Experiment (BOBMEX). The cumulus convection though being a small-scale phenomenon, still influences its embedding environment by interaction through various scales. This study shows the variation in the kinematic and convective parameters during the transition from suppressed to active periods of convection. Convergence in the lower levels and strong upward vertical velocity, significant during active convection are associated with the formation of monsoon depressions. The apparent heat source due to latent heat release and the vertical transport of the eddy heat by cumulus convection, and the apparent moisture sink due to net condensation and vertical divergence of the eddy transport of moisture, are estimated through residuals of the thermodynamic equation and examined in relation to monsoon activity during BOBMEX.

Use of AVHRR-derived surface temperatures in evaluating a land–atmosphere model

The vertical transports of heat and moisture at the Earth's surface provide a critical linkage between meteorological, hydrological and ecological processes. Unfortunately, estimates of energy and water fluxes by land surface–atmosphere models are difficult to validate. This is due to the fine spatial and temporal resolution of the models, as well as a lack of widespread observations of these fluxes and other components of the surface energy budget. However, modelled fluxes of energy and water are often based largely on accurate determination of the modelled soil surface temperature. Land surface temperatures (LSTs) derived from the Advanced Very High Resolution Radiometer (AVHRR) onboard polar-orbiting satellites can be determined over large spatial extents a few times per day. They provide a means by which modelled surface temperatures, and thus modelled fluxes, can be evaluated. In this paper, two versions of the Simulator for Hydrology and Energy Exchange at the Land Surface (SHEELS) model are evaluated using AVHRR-derived LSTs. Model vegetation cover is held constant in the first version, whereas Normalized Difference Vegetation Index (NDVI) data are used to temporally modify vegetation cover in the second version. Inclusion of the NDVI data is found to decrease the bias between modelled and satellite-derived LSTs by 0.5 K. However, even with this improvement in vegetation parametrization, bias remains large (3.7 K).

Packet Structure of Surface Eddies in the Atmospheric Boundary Layer

A smoke visualization experiment has beenperformed in the first 3,m ofneutral and unstable atmospheric boundary layersat very large Reynolds number(ReΘ > 106). Under neutral atmosphericconditions mean wind profiles agreewell with those in the canonical flatplate zero-pressure-gradient turbulentboundary layer. The experiment was designedto minimize the temperaturedifference between the passive marker (smoke)and the air to ensure that anyobserved structures were due to vortical, ratherthan buoyant, motions. Imagesacquired in the streamwise–wall-normal planeusing a planar laser light-sheetare strikingly similar to those observed inlaboratory experiments at low to moderate Reynolds numbers. They reveal large-scaleramp-like structures withdownstream inclination of 3°–35°.This inclination isinterpreted as the hairpin packet growthangle following the hairpin vortexpacket model ofAdrian, Meinhart, and Tomkins.The distribution of this characteristicangle agrees with the results of experiments at far lower Reynolds numbers,suggesting a similarity in structures among low, moderate, and high Reynoldsnumber boundary layers at vastly different scales. These results indicate thatthe hairpin vortex packet model extends over a large range of scales. Theeffect of vertical heat transport in an unstable atmosphere on wall structuresis investigated in terms of the hairpin vortex packet model.

Reconciling observations of global temperature change

It is suggested that the much publicized discrepancy between observed surface global mean temperature and global mean atmospheric temperature from 1979 to the present may be due to the fact that the atmosphere underwent a jump in temperature in 1976 (before the satellite temperature series began), and that the surface response was delayed for about a decade due to the ocean heat capacity. The ocean delay depends on both climate sensitivity and vertical heat transport within the ocean. It is shown that the observed delay is best simulated when sensitivity to doubling of CO2 is less than about 1C.

Interactions between Tropical Convection and Its Environment: An Energetics Analysis of a 2D Cloud Resolving Simulation

The phase relation between the perturbation kinetic energy (K9) associated with the tropical convection and the horizontal-mean moist available potential energy ( ) associated with environmental conditions is investigated P by an energetics analysis of a numerical experiment. This experiment is performed using a 2D cloud resolving model forced by the Tropical Ocean Global Atmosphere Coupled Ocean‐Atmosphere Response Experiment (TOGA COARE) derived vertical velocity. The imposed upward motion leads to a decrease of through the P associated vertical advective cooling, and to an increase of K9 through cloud-related processes, feeding the convection. The maximum K9 and its maximum growth rate lags and leads, respectively, the maximum imposed large-scale upward motion by about 1‐2 h, indicating that convection is phase locked with large-scale forcing. The dominant life cycle of the simulated convection is about 9 h, whereas the timescales of the imposed largescale forcing are longer than the diurnal cycle. In the convective events, the maximum growth of K9 leads the maximum decay of the perturbation moist available potential energy (P9) by about 3 h through vertical heat transport by perturbation circulation, and perturbation cloud heating. The maximum decay of P9 leads the maximum decay of by about 1 h through P the perturbation radiative processes, the horizontal-mean cloud heating, and the large-scale vertical advective cooling. Therefore, maximum gain of K9 occurs about 4‐5 h before maximum decay of . P

Vertical Transports by Plumes within the Moderately Convective Marine Atmospheric Surface Layer

Abstract Bursts in the kinematic vertical transports of heat and horizontal momentum in a moderately convective marine atmospheric surface layer are studied by applying the variable interval time averaging (VITA) detection method to principal components analysis (PCA)–decomposed datasets obtained from the Floating Instrumentation Platform (FLIP) moored vessel during the 1995 April–May Pacific Marine Boundary Layer (PMBL) experiment. For convective plumes, a well-defined dimensionless relationship is shown to exist between the vertical transports of heat and horizontal momentum; this relationship cannot be easily deduced if PCA and VITA are not both applied. PCA decomposes a dataset using correlations within that dataset instead of bandpass filtering it to retain energy in a predetermined range of scales; PCA thus respects all scales contributing to the phenomena retained in the dataset. Subsequent use of cross-spectral techniques to group the PCA-decomposed dataset into coherent structure types leads to, ...

MODELLING WATER FLOW AND SOLUTE TRANSPORT FOR HORTICULTURAL AND ENVIRONMENTAL MANAGEMENT

During the past 10 years, the simulation model SWAP (Soil, Water, Atmosphere, Plant) was developed by the Sub-Department Water Resources of Wageningen University jointly with the Department Water and Environment of Alterra Green World Research. SWAP simulates vertical transport of water, solutes and heat in variably saturated, cultivated soils at field scale level and during whole growing seasons. Different versions of the model have been applied worldwide in research, education and as a decision support tool in the management of agricultural, horticultural and natural systems water flow in homogeneous and heterogeneous soils with or without the influence of groundwater. The main features of and theoretical concepts behind SWAP are described, in particular soil water flow, solute transport and crop growth.

Dynamics of bottom boundary layers in the coastal ocean

The bottom boundary layer is the region adjacent to the sea floor, with a thickness typically on the order of meters to tens of meters, where turbulence generated by bottom drag produces vertical mixing of mass, heat, and momentum. Oceanic boundary layers are influenced not only by turbulent mixing, but also by planetary rotation, stratification, topography, surface waves, internal waves, and interaction with the erodible sea floor. Historically, understanding of the oceanic bottom boundary layer has been based on classical results in engineering and meteorology. However, recent theory and measurements have revealed unique features of oceanic boundary layers. Outstanding problems include measuring the interaction of the flow with the erodible sea floor; measuring the spatial scales of turbulent motions that accomplish vertical transport of mass, heat, and momentum; and understanding the processes that control the intensity and scale of boundary layer turbulence, particularly in stable stratification.

Airborne turbulence measurements in the lower troposphere onboard the research aircraft Dornier 128-6, D-IBUF

The research aircraft Dormer (DO) 128-6, call-sign D-IBUF, operated by the Institute of Flight Guidance and Control of the Technical University of Braunschweig and its scientific equipment is presented. The aircraft's operational capabilities and the quality of measurements of meteorological parameters and trace constituents in the lower troposphere are discussed. Besides avionic instrumentation for VFR-flights (Visual Flight Rules) and IFR-flights (Instrument Flight Rules) at low altitudes over complex terrain, there are redundant sensors for the measurement of wind, temperature and humidity. Together with INS- (Inertial Navigation System) and GPS- (Global Positioning System) navigation a sample frequency of 25 Hz (soon 100 Hz) is realised. Using a mean ground speed of 65 m s -1 , the resolution of the measurements is less than 3 m. Since 1998, the Institute of Meteorology and Climate Research at the Forschungszentrum Karlsruhe has enlarged the aircraft's research capabilities by the integration of a sensor package for the measurement of CO, NO, NO 2 . CO 2 and O 3 with frequencies between 1 Hz and 20 Hz, and detection limits of 1 ppb. The equipment does not only allow to detect mean quantities, but also, using the eddy-correlation technique, to calculate small-scale turbulent trace gas fluxes, e.g. caused by secondary circulation systems, mountain venting, convective cells and other mass transport processes between the boundary layer and the free troposphere (handover). Such data are of great importance to many aspects of air pollution dispersion and air pollution modelling. Process studies of the small-scale vertical transport of heat, moisture and trace gases and their parametrisation are some of these aspects. The function of the sensor package is shown by calibration results, intercomparison of the measurements of redundant sensors and spectral analysis of the wind components. Examples of the detection of secondary circulation systems, of the micro structure of trace gases in urban plumes and the calculation of ozone flux profiles are given.

Near‐axis subsidence rates, hydrothermal circulation, and thermal structure of mid‐ocean ridge crests

We systematically investigated near‐axis subsidence on the ridge flanks of intermediate and fast spreading mid‐ocean ridges using bathymetric data from well‐surveyed portions of the Southeast Indian Ridge (spreading at 72–76 mm/yr), the northern East Pacific Rise (91–96 mm/yr), and the southern East Pacific Rise (144 mm/yr). In all three regions, the mean subsidence rate of young (<1–1.4 Ma) seafloor is less than 220 m/m.y.1/2. The distribution of individual estimates shows a distinct peak at 180–220 m/m.y.1/2 with few profiles having subsidence rates greater than 275 m/m.y.1/2. The observed subsidence rates are significantly lower than both the worldwide average (∼350 m/m.y.1/2) and subsidence rates observed for older lithosphere at the same ridge segments. Intense hydrothermal circulation at the ridge axis can result in low subsidence rates on the adjacent ridge flanks provided the vigorous flow is confined to the immediate vicinity (<∼5 km) of the axis. According to our model, the extremely vigorous hydrothermal circulation ceases off‐axis, and conductive heat flow becomes a primary mechanism of vertical heat transport on the ridge flanks. The very low geothermal gradient within the cooled portion of the uppermost lithosphere retards conductive cooling, and the cooled area needs to be heated from below before a geothermal gradient can be established which permits significant heat to be conducted out of the lithosphere. As a result, subsidence in very young (∼0.1–1 Ma) lithosphere is suppressed. A simple one‐dimensional thermal model with a Nusselt number parameterization was used to estimate the effect of hydrothermal circulation. An upper layer with a high Nusselt number and the half‐space that it overlies are initially at a temperature of 1300°C and the surface is maintained at 0°C. After 0.1 m.y. of cooling (about 3.5 to 7 km from the spreading axis), the Nusselt number of the top layer is set to 1 so that normal conduction is simulated in the cooled layer. We used an explicit finite difference method to solve for the temporal changes in temperature with depth. This model produces subsidence rates in the range that we observe for Nu in the range of 15–30. Isotherms resulting from the modeling imply rapid lithospheric thickening very near the axis, which is incompatible with most current models for the formation of the bathymetric axial high observed at fast spreading mid‐ocean ridges.

Intense surface currents in the tropical Pacific during 1996–1998

Tropical Pacific Ocean near‐surface currents and their momentum and temperature balances are investigated using several data sets, including drifting buoy velocities and TOPEX/Poseidon altimetry. The data sets are combined to produce monthly surface current estimates on a uniform grid for the 6‐year period 1993–1998, using multivariate optimal interpolation. The analysis shows dramatic changes in current from December 1996 through August 1998 in response to the recent El Niño‐Southern Oscillation event. Eastward current anomalies of ∼1 m s−1 were recorded in December 1996 in the western Pacific, generated by sporadic westerly wind bursts. By April 1997 these equatorial anomalies reached the eastern boundary, and in the summer of 1997 a band of strong eastward flow formed across the basin. This circulation pattern persisted until the beginning of 1998, when a westward equatorial jet appeared in January‐April. Interestingly, the reversal of flow occurred prior to the restoration of the trade winds. The timing of these events as well as the results of previous dynamical studies raise questions about the relative importance of terms in the zonal momentum and temperature balances. We address the first of these questions by examining the applicability of a three‐term linear zonal momentum balance on the equator. In all cases we focus on anomalies from the time mean. Our results show that local acceleration is reasonably well balanced by the difference between zonal pressure gradient anomaly and wind‐induced momentum flux. This three‐term balance displays significant basin‐wide variations and is consistent with the conclusion that the equatorial Pacific is not in equilibrium with local wind forcing due to the presence of propagating waves. Examination of the temperature balance shows that at the beginning of El Niño the warming in the central Pacific is mainly supported by horizontal temperature transport, while the vertical heat exchange and transport become important in the eastern half of the equatorial Pacific during the transition from El Niño to La Niña.

Heat Balance in the Pacific Warm Pool Atmosphere during TOGA COARE and CEPEX

The atmosphere above the western equatorial Pacific warm pool (WP) is an important source for the dynamic and thermodynamic forcing of the atmospheric general circulation. This study uses a high-resolution reanalysis and several observational datasets including Global Precipitation Climatology Project precipitation, Tropical Ocean Global Atmosphere (TOGA) Tropical Atmosphere Ocean moored buoys, and Earth Radiation Budget Experiment, TOGA Coupled Ocean‐Atmosphere Response Experiment (COARE), and Central Equatorial Pacific Experiment (CEPEX) radiation data to examine the details of the dynamical processes that lead to this net positive forcing. The period chosen is the period of two field experiments: TOGA COARE and CEPEX during December 1992‐March 1993. The four months used in the study were sufficient to establish that the warm pool atmosphere (WPA) was close to a state of radiative‐convective‐dynamic equilibrium. The analysis suggests that the large-scale circulation imports about 200 W m22 of sensible heat and about 140 W m22 of latent energy into the WPA mainly through the low-level mass convergence and exports about 420 W m22 potential energy mainly through the upper-level mass divergence. Thus the net effect of the large-scale dynamics is to export about 80 W m22 energy out of the WPA and cool the WPA by about 0.8 K day21. The dynamic cooling in addition to the radiative cooling of about 0.4 K day21 or 40 W m22 leads to a net radiative‐dynamic cooling of about 1.2 K day21 or 120 W m22, which should be balanced by convective heating of the same magnitude. The WPA radiative cooling is only about 0.4 K day21, which is considerably smaller than previously cited values in the Tropics. This difference is largely due to the cloud radiative forcing (CRF), about 70 W m 22, associated with the deep convective cirrus clouds in the WPA, which compensates the larger clear sky radiative cooling. Thus moist convection heats the WPA, not only through the direct convective heating, that is, the vertical eddy sensible heat and latent energy transport, but also through the indirect convective heating, that is, the CRF of deep convective clouds. The CRF of the deep convective clouds has a dipole structure, in other words, strong heating of the atmosphere through convergence of longwave radiation and a comparable cooling of the surface through the reduction of shortwave radiation at the surface. As a result, the deep convective clouds enhance the required atmospheric heat transport and reduce the required oceanic heat transport significantly in the WP. A more detailed understanding of these convective processes is required to improve our understanding of the heat transport by the large-scale circulation in the Tropics.

Hydrothermal minerals and microstructures in the Silangkitang geothermal field along the Great Sumatran fault zone, Sumatra, Indonesia

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Resonant Wind-Driven Mixing in the Ocean Boundary Layer

The role of resonant wind forcing in the ocean boundary layer was examined using an ocean large-eddy simulation (LES) model. The model simulates turbulent flow in a box, measuring ∼100–300 m on a side, whose top coincides with the ocean surface. Horizontal boundary conditions are periodic, and time-dependent wind forcing is applied at the surface. Two wind forcing scenarios were studied: one with resonant winds, that is, winds that rotated at exactly the inertial frequency (at 45°N), and a second with off-resonance winds from a constant direction. The evolution of momentum and temperature for both cases showed that resonant wind forcing produces much stronger surface currents and vertical mixing in comparison to the off-resonance case. Surface wave effects were also examined and found to be of secondary importance relative to the wind forcing. The main goal was to quantify the main processes via which kinetic energy input by the wind is converted to potential energy in the form of changes in the upper-ocean temperature profile. In the resonant case, the initial pathway of wind energy was through the acceleration of an inertially rotating current. About half of the energy input into the inertial current was dissipated as the result of a turbulent energy cascade. Changes in the potential energy of the water column were ∼7% of the total input wind energy. The off-resonance case developed a much weaker inertial current system, and consequently less mixing because the wind acted to remove energy after ∼¼ inertial cycle. Local changes in the potential energy were much larger than the integrated values, signifying the vertical redistribution of water heated during the summer season. Visualization of the LES results revealed coherent eddy structures with scales from 30–150 m. The largest-scale eddies dominated the vertical transport of heat and momentum and caused enhanced entrainment at the boundary layer base. Near the surface, the dominant eddies were driven by the Stokes vortex force and had the form of Langmuir cells. Near the base of the mixed layer, turbulent motions were driven primarily by the interaction of the inertial shear with turbulent Reynolds stresses. Bulk Richardson number and eddy diffusivity profiles from the model were consistent with one-dimensional model output using the K-profile parameterization.

Vertical heat transports in the ocean and their effect on time-dependent climate change

In response to increasing atmospheric concentrations of greenhouse gases, the rate of time-dependent climate change is determined jointly by the strength of climate feedbacks and the efficiency of processes which remove heat from the surface into the deep ocean. This work examines the vertical heat transport processes in the ocean of the HADCM2 atmosphere–ocean general circulation model (AOGCM) in experiments with CO2 held constant (control) and increasing at 1 per year (anomaly). The control experiment shows that global average heat exchanges between the upper and lower ocean are dominated by the Southern Ocean, where heat is pumped downwards by the wind-driven circulation and diffuses upwards along sloping isopycnals. This is the reverse of the low-latitude balance used in upwelling–diffusion ocean models, the global average upward diffusive transport being against the temperature gradient. In the anomaly experiment, weakened convection at high latitudes leads to reduced diffusive and convective heat loss from the deep ocean, and hence to net heat uptake, since the advective heat input is less affected. Reduction of deep water production at high latitudes results in reduced upwelling of cold water at low latitudes, giving a further contribution to net heat uptake. On the global average, high-latitude processes thus have a controlling influence. The important role of diffusion highlights the need to ensure that the schemes employed in AOGCMs give an accurate representation of the relevant sub-grid-scale processes.

Thermal Equilibrium Curves and Turbulent Mixing in Keplerian Accretion Disks

We consider vertical heat transport in Keplerian accretion disks, including the effects of radiation, convection, and turbulent mixing driven by the Balbus-Hawley instability, in astronomical systems ranging from dwarf novae (DNe) and soft X-ray transients (SXTs) to active galactic nuclei (AGNs). In order to account for the interplay between convective and turbulent energy transport in a shearing environment, we propose a modified, anisotropic form of mixing-length theory that includes radiative and turbulent damping. We also include turbulent heat transport, which acts everywhere within disks, regardless of whether or not they are stably stratified and can move entropy in either direction. We have generated a series of vertical structure models and thermal equilibrium curves using the scaling law for the viscosity parameter α suggested by the exponential decay of the X-ray luminosity in SXTs. We have also included equilibrium curves for DNe using an α that is constant down to a small magnetic Reynolds number (~104). Our models indicate that weak convection is usually eliminated by turbulent radial mixing, even when mixing length estimates of convective vertical heat transport are much larger than turbulent heat transport. The substitution of turbulent heat transport for convection is more important on the unstable branches of thermal equilibrium S curves when α is larger. The low temperature turnover points Σmax on the equilibrium S curves are significantly reduced by turbulent mixing in DN and SXT disks. However, in AGN disks the standard mixing-length theory for convection is still a useful approximation when we use the scaling law for α since these disks are very thin at the relevant radii. In accordance with previous work, we find that constant α models give almost vertical S curves in the Σ-T plane and consequently imply very slow, possibly oscillating, cooling waves.

Lithosphere structure beneath the Phanerozoic intracratonic basins of North America

Four intracratonic basins of North America, the Hudson Bay, Michigan, Illinois and Williston basins, have similar ages and are close to one another. Yet, they exhibit different subsidence histories characterised by different time-scales and sediment thicknesses. They can be explained by local lithosphere thinning and by the cooling of the induced thermal anomaly. Within the framework of 1D thermal models for vertical heat transport, each basin requires a different lithosphere thickness or a different boundary condition at the base of the lithosphere. Heat flow and seismic studies show that, beneath the North American craton, the lithosphere is too thick for the assumption of purely vertical heat transfer to be valid. Thermal models are developed to account for finite thermal anomaly width and for two types of basal boundary conditions, fixed temperature or fixed heat flux. Different subsidence histories are explained by deep lithospheric anomalies of different sizes. The stability of thick continental roots requires the mantle part of the lithosphere to be compositionally buoyant with respect to ‘normal’ convecting mantle. Localised lithospheric thinning, due for example to plume penetration, results in the emplacement of compositionally denser mantle into the lithosphere. This represents a load which drives permanent flexure. The cooling time and the characteristics of flexure allow constraints on the dimensions of these deep lithospheric anomalies. There are no solutions for lithosphere thicknesses less than 170 km. The Williston and Illinois basins are associated with wide (∼200 km) and thin anomalies (∼100 km), whereas the Michigan and Hudson Bay are located on top of narrow (∼100 km) and tall (∼200 km) anomalies.