Vertical Grid Spacing Research Articles

Effects of Domain Size and Numerical Resolution on the Simulation of Shallow Cumulus Convection

The authors present three-dimensional numerical simulations of oceanic trade cumulus clouds underlying stratocumulus clouds. The case studied is a Global Energy and Water Experiment (GEWEX) Cloud System Study (GCSS) model intercomparison that is loosely based on observed conditions during the Atlantic Trade Cumulus Experiment (ATEX). It is motivated by the importance of this cloud type to global cloud radiative forcing, and their role as a feeder system for deep convection in the Tropics. This study focuses on the sensitivity of the modeled cloud field to the domain size and the grid spacing. Domain widths from 6.5 to 20 km and horizontal grid spacings ranging from 10 to 80 m, with corresponding vertical grid spacing ranging from 5 to 40 m, are studied, involving massively parallel computations on up to 2.5 billion grid cells. The combination of large domain size and small grid resolution provides an unprecedented perspective on this type of convection. The mean stratocumulus cloud fraction, optical depth, and vertical fluxes of heat, moisture, and momentum are found to be quite sensitive to both the domain size and the resolution. The sensitivities are associated with a strong feedback between cloud fraction, cloud-top radiative cooling, and entrainment. The properties of individual cumulus clouds rising into the stratocumulus are less affected than the stratocumulus clouds. The simulations with 80-m horizontal by 40-m vertical resolution are clearly under-resolved, with distinctly different distributions of liquid water within the clouds. Increasing the resolution to finer than 40 m horizontal/20 m vertical affects the inversion structure and entrainment processes somewhat, but has less impact on the structure of individual clouds. Large-domain simulations exhibit mesoscale structure in the cloud organization and liquid water path. This mesoscale variability feeds back on the domain-mean properties through the cloud-radiative feedback. These simulations suggest that very large computations are required to obtain meaningful cloud statistics for this case.

Application of the Multigrid Method and a Flexible Hybrid Coordinate in a Nonhydrostatic Model

Abstract A fully compressible, three-dimensional, nonhydrostatic model is developed using a semi-implicit scheme to avoid an extremely small time step. As a result of applying the implicit scheme to high-frequency waves, an elliptic partial differential equation (EPDE) has been introduced. A multigrid solver is applied to solve the EPDEs, which include cross-derivative terms due to terrain-following coordinate transformation. Several experiments have been performed to evaluate the model as well as the performance of the scheme with respect to tolerance number, relaxation choice, sweeps of prerelaxation and postrelaxation, and a flexible hybrid coordinate (FHC). An FHC with two functions (base and deviation functions) is introduced. The basic function provides constant vertical grid spacing required in the multigrid solver, while the deviation function helps to adjust the vertical resolution.

Simulations of phytoplankton seasonal cycle with multi-level and multi-layer physical-ecosystem models: the Black Sea example

Using the Black Sea ecosystem as an example, the phytoplankton seasonal cycle is simulated by several coupled physical-ecosystem models with different vertical resolutions, but the same biological setting. First, a high resolution multi-level model having a vertical grid spacing of about 3 m is shown to reproduce the observed annual phytoplankton structure reasonably well. This simulation is then compared with its multi-layer alternatives to investigate feasibility of using a relatively simpler model, and to look for its optimum vertical configuration. The simplest model involving a three layer structure provides only general features of the multi-level model simulation. It is able to reproduce the autumn and spring blooms taking place in the mixed layer, but it is not equally successful for simulating the summer production within the intermediate layer below the seasonal thermocline. It is found that this deficiency of the model is related to its poor nutrient recycling capability. Resolving the intermediate layer in the form of two sub-layers (i.e. increasing the model resolution to the four layer case) is shown to improve the efficiency of nutrient recycling and lead to a much better agreement of the results with those of its multi-level model. Further resolution introduced into the mixed layer, however, does not improve the performance of the layer models further. The key conclusion from our analysis is that, despite simplicity of its vertical configuration, the four layer model emerges as a practical alternative tool to its more complex, and computationally more demanding multi-level counterpart, particularly for three dimensional applications. Moreover, the Kraus–Turner type bulk surface-layer dynamics implemented in the multi-layer models are shown to be very efficient in simulating observed mixed layer characteristics as well as those deduced from the more sophisticated Mellor–Yamada level 2.5 turbulence closure parameterization of the multi-level model.

Tomographic image of low P velocity anomalies above slab in northern Cascadia subduction zone

At the Cascadia margin the Juan de Fuca plate is subducting beneath the North America plate, causing active seismicity within both plates. Earthquakes occur down to a maximum depth of 80 km within the descending oceanic plate and to about 30 km in the overriding continental plate. We use a method of seismic tomography to invert 28,230 P wave arrival times from 2666 local earthquakes that occurred in and around Vancouver Island from 1970 to 1990. The tomography model uses about 30 km horizontal and 12–19 km vertical grid spacing and assumes that the seismic velocity perturbations vary continuously between grid points. Velocity structures can be obtained to a depth of 65 km. The obtained tomographic image shows an extensive low velocity zone above the subducted slab at about 45 km depth and patches of low velocities at shallower depths just seaward of the volcanic front. The deeper extensive low velocity zone may indicate the presence of partially hydrated mantle, most likely serpentinite, as a result of slab dehydration associated with the transformation of metabasalt to eclogite. One of the shallow low velocity patches coincides with an abrupt increase in surface heat flow and may reflect the presence of partial melts or water in the crust.

Sediment-Driven Downslope Flow in Submarine Canyons and Channels: Three-Dimensional Numerical Experiments

Abstract The role of submarine canyons and channels in sediment-driven downslope flow (sediment plumes) is examined, using a three-dimensional, rotational numerical model that couples the hydrodynamics and sediment transport. The model domain consists of a bottom ocean layer of constant height coupled with an essentially inert upper ocean. The model equations are cast in a rotated, bottom-following coordinate system in which vertical grid spacing is independent of the ocean depth and bathymetry can be resolved accurately. This allows for tracing bottom-attached sediment plumes (∼decameters in height) from shallow water into great depths of the ocean. The calculations reproduce morphologic features related to the occurrance of sediment plumes, such as the formations of 1) localized deposition areas of sediment off the mouth of submarine canyons and 2) levees at both sides of submarine channels. Furthermore, it is demonstrated that sediment plumes are not only important for the transport of littoral sedimen...

Crustal structure and seismicity distribution adjacent to the Pacific and North America plate boundary in southern California

New three‐dimensional (3‐D) VP and VP/VS models are determined for southern California using P and S‐P travel times from local earthquakes and controlled sources. These models confirm existing tectonic interpretations and provide new insights into the configuration of geological structures at the Pacific‐North America plate boundary. The models extend from the U.S.‐Mexico border in the south to the southernmost Coast Ranges and Sierra Nevada in the north and have a 15‐km horizontal grid spacing and an average vertical grid spacing of 4 km, down to 22 km depth. The heterogeneity of the crustal structure as imaged by VP and VP/VS models is larger within the Pacific plate than the North American plate. Similarly, the relocated seismicity deepens and shows more complex 3‐D distribution in areas of the Pacific plate exhibiting compressional tectonics. The models reflect mapped changes in the lithology across major geological terranes such as the Mojave Desert, the Peninsular Ranges, and the Transverse Ranges. The interface between the shallow Mono of the Continental Borderland and the deep Moho of onshore California forms a broad zone to the north beneath the western Transverse Ranges, Ventura basin, and the Los Angeles basin and a narrow zone to the south, along the Peninsular Ranges. The near‐surface increase in velocity, from the surface to up to 8 km depth, is rapid and has a logarithmic shape for stable blocks and mountain ranges but is slow with a linear shape for sedimentary basins. At midcrustal depths a rapid increase in VP is imaged beneath the sediments of the large sedimentary basins, while beneath the adjacent mountain ranges the increase is small or absent.

Impact of multiple submarine channels on the descent of dense water at high latitudes

A three‐dimensional numerical hydrodynamic model is applied to examine the impact of multiple submarine channels (<10 km across, <100 m deep), common to most continental margins of the ocean, on the descent of dense water at high latitudes. The model consists of an ocean bottom layer of constant height that follows variable bottom topography under constant vertical grid spacing. An idealized continental slope of constant bottom slope is considered, including parallel channels that run perpendicular to main isobaths. The ocean is initially homogeneous and at rest. Forcing is due to a layer of dense water prescribed along the upslope boundary. When the channel aspect ratio (ratio of width to depth) exceeds the main bottom slope, dense water is carried downslope by narrow channel plumes centered along the channel axes. Owing to a small internal Rossby radius less than the channel width the plume dynamics are governed by a geostrophic balance across the channels. Interaction of adjacent channel plumes leads to complex bottom‐parallel circulations. The net downslope density flux resulting from these circulations exceeds that of viscous (ageostrophic) flow of dense water developing without channels. When the channel aspect ratio is less than the main bottom slope, the descent of dense water is dominated by viscous flow. Narrow geostrophic circulation patterns along channels, superimposed on the mean flow, however, induce advective entrainment of lighter ambient water across the leading density front of descending water. As a result of this, the net downslope density flux is reduced as compared to that without channels. Sensitivity studies reveal that the channel‐modified dynamics are independent of the magnitude of the eddy viscosity.

NUNERICAL SIMULATION OF GYRES IN LAKE BIWA

The formation process of three gyres in Lake Biwa, as observed using ADCP, has been simulated by using Large Eddy Simulation (LES). Two different dynamic subgrid-scale (SOS) models-Dynamic Mixed Model (DMM) and Mixed Scaling Formulation Model (MSFM)- are employed to describe stratified non-isotropic SGS stress due to the large disproportion between horizontal and vertical gridspacing in the computational grid.The driving force of gyre formation is assumed to be differential heating due to heat volume differences between middle-lake and shoreline areas. This condition was created in the simulation by setting the initial temperature distribution in the lake based on field observations. Significant gyre formation patterns are calculated by LES both with DMM and MSFM. Due to the huge disproportion between horizontal and vertical grid spacing, the isotropic SGS model (such as the Smagorinsky Model) does not perform well.

Evaluation of the Kinetic Energy Approach for Modeling Turbulent Fluxesin Stratocumulus

Abstract The modeling of vertical mixing by a turbulence scheme on the basis of prognostic turbulent kinetic energy (E) and a diagnostic length scale (l) is investigated with particular emphasis on the representation of entrainment. The behavior of this E–l scheme is evaluated for a stratocumulus case observed in the Atlantic Stratocumulus Transition Experiment, and a comparison is made with the results of large eddy simulation models for the same case. It appears that the E–l model is well capable of reproducing the main features of vertical mixing and entrainment. This is the case with a high vertical grid spacing of 25 m and a short time step of 1 s, even with a relatively simple formulation for the turbulent length scale. However, the model results degenerate rapidly on coarse temporal and spatial resolution. For time steps on the order of 1 min it is shown that the process-splitting time integration scheme (in which the tendencies due to turbulent diffusion and radiation are computed independently) r...

Currents at the light-vessel “Deutsche Bucht”: A comparison between ADCP measurements and the BSH forecast model

Between June 15 and August 10,1999, an Acoustic Doppler Current Profiler (ADCP) and a water level recorder (WLR) were deployed in the close vicinity of the unmanned light-vessel “Deutsche Bucht” in the German Bight. Together with locally recorded meteorological and hydrographical data (salinity and temperature), this in-situ data set is compared to the forecasts of the BSH circulation model “BSHcmod”. The meteorological measurements are used to assess the meteorological model input generated by an atmospheric model of the German Weather Service. Generally, we observed a good agreement between in-situ and model data. Differences between measured and predicted currents were observed at the surface and at mid-depth. They were caused mainly by missing ADCP data within the first 3 metres under the surface and by the coarse vertical grid spacing of the model which prevents the representation of sharp vertical gradients.

A coupled ice–ocean model for the Greenland, Iceland and Norwegian Seas

Simulations from a coupled ice–ocean model that highlight the importance of synoptic forcing on sea-ice dynamics are described. The ocean model is a non-hydrostatic primitive equation model coupled to a dynamic thermodynamic sea ice model. The ice modelling sensitivity study presented here is part of an ongoing research programme to define the role played by sea ice in the energy balance of the Greenland Sea. The different categories of sea ice found in the subpolar regions are simulated through the use of equations for thin ice, thick ice and the Marginal Ice Zone. A basin scale numerical model of the Greenland, Iceland and Norwegian Seas has a horizontal resolution of 20 km and a vertical grid spacing of 50 m. This resolution is adequate for resolving the mesoscale topographic structures known to control the circulation in this region. The spin-up reproduces the main features of the circulation, including the cyclonic gyres in the Norwegian and Greenland Basins and Iceland Plateau. Topographic steering of the flow is evident. The baroclinic Rossby radius of deformation is between 5 and 10 km so that the model is not eddy-resolving. The coupled ice–ocean model was run for a period of two weeks. The influence of horizontal resolution of the atmospheric model was tested by comparing simulations using six hourly wind fields from the ECMWF with those generated using six hourly fields from a HIRLAM, with horizontal resolutions of 1° and 0.18° respectively. The simulations show reasonable agreement with satellite ice compactness data and data of ice transports across sections at 79°N, 75°N and Denmark Strait.

A grid generating algorithm for simulating a fluctuating water table boundary in heterogeneous unconfined aquifers

An algorithm is presented for generating finite element grids that can be used to calculate the position of a fluctuating water table and the formation of seepage faces within a heterogeneous unconfined aquifer. Our approach overcomes limitations with existing techniques by allowing the water table to rise or decline through hydrostratigraphic boundaries yet maintains numerical and conceptual accuracy with respect to hydrostratigraphic geometry. The algorithm involves (1) limited stretching or shrinking of elements along the water table if the change in the position of the water table is small with respect to the vertical grid spacing, and (2) the addition or removal of nodes and elements in the finite element mesh along the water table as the change becomes large with respect to the vertical grid spacing. This technique is applicable to any 2-D or 3-D finite element code that contains an automatic finite-element grid generator.

An intercomparison of radiatively driven entrainment and turbulence in a smoke cloud, as simulated by different numerical models

As part of a programme of intercomparison of eddy-resolving and one-dimensional (1-D) boundary-layer models, a convective boundary-layer filled with radiatively active ‘smoke’ was simulated. the programme is sponsored by the Global Energy and Water Experiment Cloud Systems Study. Cloud-top-cooling rates weire chosen to be comparable with those observed in marine stratocumulus, while avoiding evaporative feedbacks on entrainment and turbulence that are also important in liquid-water clouds. the radiative-cooling rate hacl a specified dependence on the smoke profile, so that differences between simulations could only be a result of different numerical representations of fluid motion and subgrid-scale turbulence. At a workshop in De Bilt, the Netherlands in August 1995, results from numerous groups around the world were compared with each other and with a previously investigated laboratory analogue to the smoke cloud. The intercomparison results show that models must be run with higher vertical resolution in the inversion than is customary at present, in order to accurately simulate the entrainment rate into cloud-topped bounday-layers under strong inversions. In three-dimensional (3-D) models using a vertical grid spacing of 5-12.5 m, sufficient to resolve the horizontal variability of inversion height, entrainment rates were 10-50% larger than: he range consistent with the laboratory experiments. With a larger vertical grid spacing of 25 m, 1-D, 2-D and 3-D models all overestimated the entrainment rate by more than 50%. 3-D models with monotone advection-schemes overestimated entrainment slightly more than those with non-monotone schemes, at least when 25 m vertical grid-spacing was used. However, results from non-monotone schemes had several undesirable features associated hith the generation of undershoots and overshoots, most notably spurious turbulent mixing above the smoke layer. the 1-D models tended to underestimate turbulent kinetic energy (TKE) but performed reasonably well given tkeir simplicity. 2-D models produced too much entrainment and considerably overestimated TKE, compared with 3-D models with the same numerical formulation. Based on a simple scaling-argument, we propose that the minimum vertical grid-spacing required to obtain an accurate entrainment-rate is of the order of the horizontal fluctuations in inversion height, which is proportional to the layer-averaged TKE and inversely proportional to the inversion strength.

An intercomparison of radiatively driven entrainment and turbulence in a smoke cloud, as simulated by different numerical models

AbstractAs part of a programme of intercomparison of eddy‐resolving and one‐dimensional (1‐D) boundary‐layer models, a convective boundary‐layer filled with radiatively active ‘smoke’ was simulated. the programme is sponsored by the Global Energy and Water Experiment Cloud Systems Study. Cloud‐top‐cooling rates weire chosen to be comparable with those observed in marine stratocumulus, while avoiding evaporative feedbacks on entrainment and turbulence that are also important in liquid‐water clouds. the radiative‐cooling rate hacl a specified dependence on the smoke profile, so that differences between simulations could only be a result of different numerical representations of fluid motion and subgrid‐scale turbulence. At a workshop in De Bilt, the Netherlands in August 1995, results from numerous groups around the world were compared with each other and with a previously investigated laboratory analogue to the smoke cloud.The intercomparison results show that models must be run with higher vertical resolution in the inversion than is customary at present, in order to accurately simulate the entrainment rate into cloud‐topped bounday‐layers under strong inversions. In three‐dimensional (3‐D) models using a vertical grid spacing of 5‐12.5 m, sufficient to resolve the horizontal variability of inversion height, entrainment rates were 10‐50% larger than: he range consistent with the laboratory experiments. With a larger vertical grid spacing of 25 m, 1‐D, 2‐D and 3‐D models all overestimated the entrainment rate by more than 50%. 3‐D models with monotone advection‐schemes overestimated entrainment slightly more than those with non‐monotone schemes, at least when 25 m vertical grid‐spacing was used. However, results from non‐monotone schemes had several undesirable features associated hith the generation of undershoots and overshoots, most notably spurious turbulent mixing above the smoke layer. the 1‐D models tended to underestimate turbulent kinetic energy (TKE) but performed reasonably well given tkeir simplicity. 2‐D models produced too much entrainment and considerably overestimated TKE, compared with 3‐D models with the same numerical formulation.Based on a simple scaling‐argument, we propose that the minimum vertical grid‐spacing required to obtain an accurate entrainment‐rate is of the order of the horizontal fluctuations in inversion height, which is proportional to the layer‐averaged TKE and inversely proportional to the inversion strength.

Simulation of Density-Driven Frictional Downslope Flow inZ-Coordinate Ocean Models

An important component of the ocean’s thermohaline circulation is the sinking of dense water from continental shelves to abyssal depths. Such downslope flow is thought to be a consequence of bottom stress retarding the alongslope flow of density-driven plumes. In this paper the authors explore the potential for explicitly simulating this simple mechanism in z-coordinate models. A series of experiments are performed using a twin density-coordinate model simulation as a standard of comparison. The adiabatic nature of the experiments and the importance of bottom slope make it more likely that the density-coordinate model will faithfully reproduce the solution. The difficulty of maintaining the density signal as the plume descends the slope is found to be the main impediment to accurate simulation in the z-coordinate model. The results of process experiments suggest that the model solutions will converge when the z-coordinate model has sufficient vertical resolution to resolve the bottom viscous layer and horizontal grid spacing equal to its vertical grid spacing divided by the maximum slope. When this criterion is met it is shown that the z-coordinate model converges to an analytical solution for a simple two-dimensional flow.

Improved Green’s function parabolic equation method for atmospheric sound propagation

The numerical implementation of the Green’s function parabolic equation (GFPE) method for atmospheric sound propagation is discussed. Four types of numerical errors are distinguished: (i) errors in the forward Fourier transform; (ii) errors in the inverse Fourier transform; (iii) errors in the refraction factor; and (iv) errors caused by the split-step approximation. The sizes of the errors depend on the choice of the numerical parameters, in particular the range step and the vertical grid spacing. It is shown that this dependence is related to the stationary phase point of the inverse Fourier integral. The errors of type (i) can be reduced by increasing the range step and/or decreasing the vertical grid spacing, but can be reduced much more efficiently by using an improved approximation for the forward Fourier integral. The errors of type (ii) can be reduced by using a numerical filter in the inverse Fourier integral. The errors of type (iii) can be reduced slightly by using an improved refraction factor. The errors of type (iv) can be reduced only by reducing the range step. The reduction of the four types of errors is illustrated for realistic test cases, by comparison with analytic solutions and results of the Crank–Nicholson PE (CNPE) method. Further, optimized values are presented for the parameters that determine the computational speed of the GFPE method. The computational speed difference between GFPE and CNPE is discussed in terms of numbers of floating point operations required by both methods.

Accuracy of numerical methods for solving the advection–diffusion equation as applied to spore and insect dispersal

Three algorithms for solving a simplified 3-D advection–diffusion equation were compared as to their accuracy and speed in the context of insect and spore dispersal. The algorithms tested were the explicit central difference (ECD) method, the implicit Crank–Nicholson (ICN) method, and the implicit Chapeau function (ICF) method. The three algorithms were used only to simulate the diffusion process. A hold-release wind shifting method was developed to simulate the wind advection process, which shifts the concentration an integer number of grids and accumulates the remaining wind travel distance (which is less than the grid spacing) to the next time step. The test problem was the dispersal of a cloud of particles (originally in only one grid cell) in a 3-D space. The major criterion for testing the accuracy was R 2, which represents the proportion of the total variation in particle distribution in all grid cells that is accounted for by the particle distribution through numerical solutions. Other criteria included total remaining mass, peak positive density, and largest negative density. High R 2 values were obtained for the ECD method with (Δ t K z)/(Δ z) 2≤0.5 (Δ t=time step; K z=vertical eddy diffusion coefficient; Δ z=vertical grid spacing), and for the two implicit methods with Δ t K z/(Δ z) 2≤5. The ICN method gave higher R 2 values than the ICF method when the concentration gradients were high, but its accuracy decreased more rapidly with the progress of time than the ICF method with a combination of a large grid spacing and a large time step. With very steep concentration gradients, the ICF method generated huge negative values, the ICN method generated negative values to a lesser extent, and the ECD method generated only small negative values. It was also found that good mass and/or peak preservation did not necessarily correspond to a higher R 2 value. Based on the R 2 value and the requirement for concentration positivity, for simulations with steep concentration gradients, the ECD method would be most appropriate, followed by the ICN method, and the ICF method would be least appropriate due to large negative values. For simulations with low concentration gradients, the ECD or ICF or ICN method could be used, but the ICN method would not be appropriate for use in a combination of a large time step and a large grid spacing. The results from this study could help selection and use of appropriate numerical methods in studying the spatial dynamics of spores and insects.

Generation of fast timescale phenomena in thermo-mechanical processes

We have studied thermo-mechanical mechanisms for producing fast timescale geological processes. A two-dimensional time-dependent convection model with the extended-Boussinesq approximation has been used in which both viscous and adiabatic heating are included. Both non-Newtonian and Newtonian temperature- and depth-dependent rheologies with a depth-dependent thermal expansivity have been considered. A fourth-order accurate scheme has been used with a vertical grid spacing as fine as 3 km being imposed in the upper portion of the mantle, and a horizontal grid spacing of around 10 km. Non-Newtonian rheology precipitates the development of very fast upwellings with large amounts of attendant viscous heating and high surface heat flow. Thermal instabilities with fast timescales occur near the surface during the plume impingement. The growth times of these instabilities are found to decrease significantly with the power-law index n and the convective vigor, and increase with larger surface dissipation number. For n = 3 the characteristic timescales are on the order of 1 Myr. Instabilities produced with Newtonian rheology occur over longer timescales. Non-Newtonian rheology also enhances the production of viscous heating to a magnitude which can be 10 4 times greater than that for chondritic heating. These results suggest that rapid geological events, less than 1 Myr, can be achieved with a non-Newtonian, temperature-dependent rheology by means of a positive thermo-mechanical feedback.

A numerical simulation of flow at Fieberling Guyot

A numerical sigma‐coordinate ocean circulation model is used to investigate tidally forced flow near Fieberling Guyot. The aim is to reproduce the observed currents and to identify the dominant physical mechanisms that lead to the complex three‐dimensional flow fields at this tall and steep seamount in the northeast Pacific. Our very high resolution simulation (with 500 m horizontal and less than 20 m vertical grid spacing in the vicinity of the seamount summit) was performed with the newest version of the terrain‐following sigma‐coordinate primitive equation model (SPEM). As in previous more idealized studies, the seamount was placed in the center of a uniformly rotating periodic channel and forced by diurnal barotropic tides. The exponential initial stratification, the tidal forcing amplitude, and its orientation were chosen based on observations from the Fieberling area. Three major characteristics of the flow observed at Fieberling Guyot are reproduced both qualitatively and quantitatively: diurnal currents reach about 20 cm s−1, a twentyfold amplification relative to the tidal flow away from the seamount; the time‐mean anticyclonic flow speeds are close to the observed 10 cm s−1 maximum azimuthal velocity; and the spatial structure of this vortex shows a maximum at about 6 km radius between 400 and 600 m depth, clearly lifted off the bottom. The time‐mean flows are found to be maintained by diurnal waves of a mixed type: the net motion shows characteristics of both bottom‐intensified seamount trapped waves and vertically propagating vortex trapped waves. While the former are mainly responsible for setting up a time‐mean anticyclonic flow along the upper flanks at the bottom, the latter are needed to redistribute the momentum and time‐mean density, thereby reproducing the observed structure with a flow maximum off the bottom. An analysis of the energy, momentum, and density fluxes shows that rectification depends critically on the eddy fluxes that balance the time‐mean downwelling over the seamount summit and upper flanks. The results of sensitivity and parameter studies are utilized to further interpret the role of individual physical mechanisms and the time‐mean dynamical balances.

Application of transilient turbulent theory to study interactions between the atmospheric boundary layer and forest canopies

The new Forest-Land-Atmosphere ModEl called FLAME is presented. The first-order, nonlocal turbulence closure called transilient turbulence theory (Stull, 1993) is applied to study the interactions between a forested land-surface and the atmospheric boundary layer (ABL). The transilient scheme is used for unequal vertical grid spacing and includes the effects of drag, wake turbulence, and interference to vertical mixing by plant elements. Radiation transfer within the vegetation and the equations for the energy balance at the leaf surface have been taken from Norman (1979). Among others, the model predicts profiles of air temperature, humidity and wind velocity within the ABL, sensible and latent heat fluxes from the soil and the vegetation, the stomata and aerodynamic resistances, as well as profiles of temperature and water content in the soil. Preliminary studies carried out for a cloud free day and idealized initial conditions are presented. The canopy height is 30 m within a vertical domain of 3 km. The model is able to capture some of the effects usually observed within and above forested areas, including the relative wind speed maximum in the trunk space and the counter gradient-fluxes in the lower part of the plant stand. Of special interest is the determination of the location and magnitude of the turbulent mixing between model layers, which permits one to identify the effects of large eddies transporting momentum and scalar quantities into the canopy. A comparison between model simulations and field measurements will be presented in a future paper.