On eddy diffusion profiles in oceanic bottom boundary layers associated with cold eddies and filaments

The oceanic bottom boundary-layer model of Weatherly and Martin (1978) is used to study the vertical structure of the eddy diffusivity in a region with initially imposed bottom mixed-layer thickness. Because of near-bottom oceanic features, such as the Cold Filament (Weatherly and Kelley, 1982) and cold eddies (Ebbesmeyer et al., 1988), the bottom mixed-layer thickness is not the sole result of boundary-layer mixing; this is the incentive for this study. For a given geostrophic forcing and imposed mixed-layer depth, a formula for the eddy diffusion coefficient is found. This parameterization of the eddy diffusivity improves previous formulas used in oceanic and atmospheric boundary layers in the upper portion of the boundary layer. A simple model of a Cold Filament-like feature demonstrates the structure of the bottom boundary layer, the bottom mixed layer, and the relation between the two. A lens-like cross section of cold blobs, often used in analytical models, may be inappropriate if bottom friction is important.     

Theory And Measurements For Turbulence Spectra And Variances In The Atmospheric Neutral Surface Layer

Predictions from a new theory for high Reynolds number turbulent boundary layers during near-neutral conditions are shown to agree well with measurements of atmospheric surface-layer variances and spectra. The theory suggests surface-layer turbulence is determined by detached eddies that largely originate in the shearing motion immediately above the surface layer; as they descend into this layer, they are strongly distorted by the local shear and impinge onto the surface. Because the origin of these eddies is non-local, they are similar to those described in previous studies as `inactive' turbulence. However, they are, in fact, dynamically highly active, supplying the major mechanism for the momentum transport, including upward bursting on the time scale of the larger eddies. The vertical velocity results show that the variance and the low frequency parts of spectra increase with height in the surface layer, while in the self similar (k₁ ^-1) range the streamwise low frequency components are approximately constant with height. These large-scale longitudinal eddies extend to a length _s, which is equal to the boundary-layer height near the surface andincreases linearly to a maximum of about three times the boundary-layer height at roughly 15 m and decreases in the upper parts of the surface layer. This lower part of the surface layer, the eddy surface layer, is the region in which the eddies impinging from layers above are strongly distorted. This new result for the atmospheric boundary layer has practical application for calculating fluctuating wind loads on structures and lateral dispersion of pollution from local sources.     

Simulation of monsoon boundary-layer processes using a regional scale nested grid model

A nested grid regional model with a high vertical resolution in the atmospheric boundary layer is used to simulate various atmospheric processes during an active monsoon period. A turbulence kinetic energy closure scheme is used to predict the boundary-layer structure. Model predictions indicate different structures of the boundary layer over land and oceans, as observed. Significant diurnal variation in boundary-layer structure and associated processes is predicted over land and negligible variations over oceans. The Somali jet over the Arabian Sea is well predicted. Location of the predicted monsoon depression and the associated rainfall are in good agreement with the observations. Also, predicted rainfall and its spatial distribution along the west coast of India are in good agreement with the observations.     

A grid nesting method for large-eddy simulation of planetary boundary-layer flows

A method for performing nested grid calculations with a large-eddy simulation code is described. A common numerical method is used for all meshes, and the grid architecture consists of a single outer or coarse grid, and nested or fine grids, which overlap in some common region. Inter-grid communication matches the velocity, pressure and potential temperature fields in the overlap region. Resolved and sub-grid scale (SGS) turbulent fluxes and kinetic energy on the fine grid are averaged to the coarse grid using a conservation rule equivalent to Germano's identity used to develop dynamic SGS models.Simulations of a slightly convective, strong shear planetary boundary layer were carried out with varying surface-layer resolutions. Grid refinements in the (x, y, z) directions of up to (5, 5, 2) times were employed. Two-way interaction solutions on the coarse and fine meshes are successfully matched in the overlap region on an instantaneous basis, and the turbulent motions on the fine grid blend smoothly into the coarse grid across the grid interface. With surface-layer grid nesting, significant increases in resolved eddy fluxes and variances are found. The energy-scale content of the vertical velocity, and hence vertical turbulent fluxes, appear to be most influenced by increased grid resolution. Vertical velocity spectra show that the dominant scale shifts towards higher wavenumbers (smaller scales) and the magnitude of the peak energy is increased by more than a factor of 3 with finer resolution. Outside of the nested region the average heat and momentum fluxes and spectra are slightly influenced by the fine resolution in the surface layer. From these results we conclude that fine resolution is required to resolve the details of the turbulent motions in the surface layer. At the same time, however, increased resolution in the surface layer does not appreciably alter the ensemble statistics of the resolved and SGS motions outside of the nested region.     

A Case Study on the Effects of Heterogeneous Soil Moisture on Mesoscale Boundary-Layer Structure in the Southern Great Plains, U.S.A. Part II: Mesoscale Modelling

The importance of soil moisture inputs and improved model physics in the prediction of the daytime boundary-layer structure during the Southern Great Plains Hydrology Experiment 1997 (SGP97) is investigated using the non-hydrostatic fifth-generation Pennsylvania State University/National Center for Atmospheric Research (PSU/NCAR) Mesoscale Model MM5. This is Part II of a two-part study examining the relationship of surface heterogeneity to observed boundary-layer structure. Part I focuses on observations and utilizes a simple model while Part II uses observations and MM5 modelling. Soil moisture inputs tested include a lookup table based on soil type and season, output from an offline land-surface model (LSM) forced by atmospheric observations, and high-resolution ( 800 m) airborne microwave remotely sensed data. Model physics improvements are investigated by comparing an LSM directly coupled with the MM5 to a simpler force-restore method at the surface. The scale of land surface heterogeneities is compared to the scale of their effects on boundary-layer structure.The use of more detailed soil moisture fields allowed the MM5 to better represent the large-scale (hundreds of km) and small-scale (tens of km) horizontal gradients in surface-layer weather and, to a lesser degree, the atmospheric boundary-layer (ABL) height, which was evaluated against observations measured by differential absorption lidar (DIAL). The benefits of coupling an LSM to the MM5 were not readily evident in this summertime case, with the model having particular difficulty simulating the timing of maximum surface fluxes while underestimating the depth of the mixed layer.     

Estimation of the average surface heat flux over an inhomogeneous terrain from the vertical velocity variance

An indirect method of estimating the surface heat flux from observations of vertical velocity variance at the lower mid-levels of the convective atmospheric boundary layer is described. Comparison of surface heat flux estimates with those from boundary-layer heating rates is good, and this method seems to be especially suitable for inhomogeneous terrain for which the surface-layer profile method cannot be used.     

The Air Force Global Weather Central operational boundary-layer model

A limited-area seven-layer physical-numerical model for the lower tropospheric region (surface - 1600m) is described. The grid interval, approximately 190km, is half that of the standard numerical weather-prediction grid used in the hemispheric free atmospheric operational model at the Air Force Global Weather Central (AFGWC). This model is an integral part of the complete AFGWC meso-scale (sub-synoptic) numerical analysis and prediction system and is used to provide greater horizontal and vertical resolution in both numerical analyses and forecasts.Important features of this boundary-layer model include: a completely automated objective analysis of input data; the transport of heat and moisture by three-dimensional wind flow; latent heat exchange in water substance phase changes; and eddy fluxes of heat and water vapor.Input data are conventional synoptic surface and upper air reports. Other operational AFGWC prediction models provide input in the form of horizontal wind components at the upper boundary and an estimate of cloudiness above the boundary layer. Forecasts for the lower boundary and surface layer are empirically derived. Despite some approximations which broadly simplify the real planetary boundary-layer processes, operational use for highly weather-sensitive Air Weather Service support indicates that the model is capable of producing accurate detailed forecasts for periods of up to 24h.A modified version of this paper was presented at the IUGG-IAMAP-AMS conference on Planetary Boundary Layers at Boulder, Colo., 18–21 March, 1970, and at the 5th annual Congress of the Canadian Meteorological Society, at Macdonald College, 12–14 May, 1971.     

A simple unified theory for flow in the canopy and roughness sublayer

The mean flow profile within and above a tall canopy is well known to violate the standard boundary-layer flux–gradient relationships. Here we present a theory for the flow profile that is comprised of a canopy model coupled to a modified surface-layer model. The coupling between the two components and the modifications to the surface-layer profiles are formulated through the mixing layer analogy for the flow at a canopy top. This analogy provides an additional length scale—the vorticity thickness—upon which the flow just above the canopy, within the so-called roughness sublayer, depends. A natural form for the vertical profiles within the roughness sublayer follows that overcomes problems with many earlier forms in the literature. Predictions of the mean flow profiles are shown to match observations over a range of canopy types and stabilities. The unified theory predicts that key parameters, such as the displacement height and roughness length, have a significant dependence on the boundary-layer stability. Assuming one of these parameters a priori leads to the incorrect variation with stability of the others and incorrect predictions of the mean wind speed profile. The roughness sublayer has a greater impact on the mean wind speed in stable than unstable conditions. The presence of a roughness sublayer also allows the surface to exert a greater drag on the boundary layer for an equivalent value of the near-surface wind speed than would otherwise occur. This characteristic would alter predictions of the evolution of the boundary layer and surface states if included within numerical weather prediction models.     

Comparing mixing-length models of the diabatic wind profile over homogeneous terrain

Models of the diabatic wind profile over homogeneous terrain for the entire atmospheric boundary layer are developed using mixing-length theory and are compared to wind speed observations up to 300 m at the National Test Station for Wind Turbines at Høvsøre, Denmark. The measurements are performed within a wide range of atmospheric stability conditions, which allows a comparison of the models with the average wind profile computed in seven stability classes, showing a better agreement than compared to the traditional surface-layer wind profile. The wind profile is measured by combining cup anemometer and lidar observations, showing good agreement at the overlapping heights. The height of the boundary layer, a parameter required for the wind profile models, is estimated under neutral and stable conditions using surface-layer turbulence measurements, and under unstable conditions based on the aerosol backscatter profile from ceilometer observations.     

A Model of the Planetary Boundary Layer Over a Snow Surface

A model of the planetary boundary layer over a snow surface has been developed. It contains the vertical heat exchange processes due to radiation, conduction, and atmospheric turbulence. Parametrization of the boundary layer is based on similarity functions developed by Hoffert and Sud (1976), which involve a dimensionless variable, ζ, dependent on boundary-layer height and a localized Monin-Obukhov length. The model also contains the atmospheric surface layer and the snowpack itself, where snowmelt and snow evaporation are calculated. The results indicate a strong dependence of surface temperatures, especially at night, on the bursts of turbulence which result from the frictional damping of surface-layer winds during periods of high stability, as described by Businger (1973). The model also shows the cooling and drying effect of the snow on the atmosphere, which may be the mechanism for air mass transformation in sub-Arctic regions.     

A model of the planetary boundary layer over a snow surface

A model of the planetary boundary layer over a snow surface has been developed. It contains the vertical heat exchange processes due to radiation, conduction, and atmospheric turbulence. Parametrization of the boundary layer is based on similarity functions developed by Hoffert and Sud (1976), which involve a dimensionless variable, ζ, dependent on boundary-layer height and a localized Monin-Obukhov length. The model also contains the atmospheric surface layer and the snowpack itself, where snowmelt and snow evaporation are calculated. The results indicate a strong dependence of surface temperatures, especially at night, on the bursts of turbulence which result from the frictional damping of surface-layer winds during periods of high stability, as described by Businger (1973). The model also shows the cooling and drying effect of the snow on the atmosphere, which may be the mechanism for air mass transformation in sub-Arctic regions.     

A coupled surface boundary-layer-quasigeostrophic model

A three-dimensional model of the mesoscale surface boundary layer of the open ocean is developed through scale analysis of the primitive equations with mixing included. A set of surface boundary-layer equations appropriate for a broad range of oceanic and atmospheric scales is thereby derived. The essential basis of the model is a coupling between quasigeostrophic dynamics away from the boundary layer and arbitrary mixing models within the mixed layer. The coupling consists of advection of the boundary layer by the horizontal and vertical components of the interior quasigeostrophic flow and forcing of the interior by the boundary layer in the form of divergence within the boundary layer which leads to vortex stretching/compression in the interior. The divergence is generalized for mesoscale wind-driven flows and includes nonlinear interaction between the directly wind-driven boundary-layer flow and the interior flow in the form of interior relative vorticity advection by the wind-driven flow. The nature of the equations leads us to apply a numerical algorithm to their solution. This algorithm is calibrated through application to idealized problems to determine the temporal and spatial grid requirements. The model is initialized with a realistic ocean flow having the properties of the Gulf Stream.     

Large-Eddy Simulation of the Stable Atmospheric Boundary Layer using Dynamic Models with Different Averaging Schemes

Large-eddy simulation (LES) of a stable atmospheric boundary layer is performed using recently developed dynamic subgrid-scale (SGS) models. These models not only calculate the Smagorinsky coefficient and SGS Prandtl number dynamically based on the smallest resolved motions in the flow, they also allow for scale dependence of those coefficients. This dynamic calculation requires statistical averaging for numerical stability. Here, we evaluate three commonly used averaging schemes in stable atmospheric boundary-layer simulations: averaging over horizontal planes, over adjacent grid points, and following fluid particle trajectories. Particular attention is focused on assessing the effect of the different averaging methods on resolved flow statistics and SGS model coefficients. Our results indicate that averaging schemes that allow the coefficients to fluctuate locally give results that are in better agreement with boundary-layer similarity theory and previous LES studies. Even among models that are local, the averaging method is found to affect model coefficient probability density function distributions and turbulent spectra of the resolved velocity and temperature fields. Overall, averaging along fluid pathlines is found to produce the best combination of self consistent model coefficients, first- and second-order flow statistics and insensitivity to grid resolution.     

Towards urbanisation of the non-hydrostatic numerical weather prediction model Lokalmodell (LM)

Numerical weather prediction models are increasingly employed for providing meteorological data for urban air quality applications. Model resolution, physiographic parameters and surface-layer parameterisations need to be adapted to the requirements of the urban boundary layer. The Lokalmodell of the German Weather Service was triple-nested down to a horizontal grid resolution of 1.1 km, urbanised physiographic parameters were implemented, and an additional anthropogenic heat source was introduced. Results of a sensitivity study for a spring dust episode in Helsinki show a clear urbanisation effect of these measures on temperature, humidity and the partitioning of surface fluxes, leading to an increased Bowen ratio and heat storage and an urban heat island effect.     

Marine Boundary Layer And Turbulent Fluxes Over The Baltic Sea: Measurements And Modelling

Two weeks of measurements of the boundary-layer height over a small island (Christiansø) in the Baltic Sea are discussed. The meteorological conditions are characterised by positive heat flux over the sea. The boundary-layer height was simulated with two models, a simple applied high-resolution (2 km × 2 km) model, and the operational numerical weather prediction model HIRLAM (grid resolution of 22.5 km × 22.5 km). For southwesterly winds it was foundthat a relatively large island (Bornholm) lying 20-km upwind of the measuring site influences the boundary-layer height. In this situation the high-resolution simple applied model reproduces the characteristics of the boundary-layer height over the measuring site. Richardson-number based methods using data from simulations with the HIRLAM model fail, most likely because the island and the water fetch to the measuring site are about the size of the grid resolution of the HIRLAM model and therefore poorly resolved. For northerly winds, the water fetch to the measuring site is about 100 km. Both models reproduce the characteristics of the height of the marine boundary layer. This suggests that the HIRLAM model adequately resolves a water fetch of 100 km with respect to predictions of the height of the marine boundary layer.     

Characteristics and Numerical Simulations of Extremely Large Atmospheric Boundary-layer Heights over an Arid Region in North-west China

Over arid regions in north-west China, the atmospheric boundary layer can be extremely high during daytime in late spring and summer. For instance, the depth of the observed convective boundary layer can exceed 3,000 m or even be up to 4,000 m at some stations. In order to characterize the atmospheric boundary-layer (ABL) conditions and to understand the mechanisms that produce such an extreme boundary-layer height, an advanced research version of the community weather research and forecasting numerical model (WRF) is employed to simulate observed extreme boundary-layer heights in May 2000. The ability of the WRF model in simulating the atmospheric boundary layer over arid areas is evaluated. Several key parameters that contribute to the extremely deep boundary layer are identified through sensitivity experiments, and it is found that the WRF model is able to capture characteristics of the observed deep atmospheric boundary layer. Results demonstrate the influence of soil moisture and surface albedo on the simulation of the extremely deep boundary layer. In addition, the choice of land-surface model and forecast lead times also plays a role in the accurate numerical simulation of the ABL height.     

Nocturnal boundary-layer height: Observations by acoustic sounders and predictions in terms of surface-layer parameters

Acoustic sounder measurements of the stable boundary-layer height taken during the EPRI Plume Model Validation and Development Project experiment are examined. Comparison of simultaneous measurements by two sodars located 15 km apart shows good agreement. Several widely used diagnostic formulas for estimation of the boundary-layer height, based on wind speed and surface-layer parameters, such as friction velocity and Monin-Obukhov length, are tested against the sodar data. Of these, best performance is found using a simple linear relationship with friction velocity or, alternatively, wind speed at 10 m height. No evidence is found to support the more often used Zilitinkevich (1972) formula. Tests using selected data from the Cabauw site in the Netherlands confirm the results found on the basis of EPRI data.     

A GCSS Boundary-Layer Cloud Model Intercomparison Study Of The First Astex Lagrangian Experiment

Three single-column models (all with an explicit liquid water budget and compara-tively high vertical resolution) and three two-dimensional eddy-resolving models (including one with bin-resolved microphysics) are compared with observations from the first ASTEX Lagrangian experiment. This intercomparison was a part of the second GCSS boundary-layer cloud modelling workshop in August 1995.In the air column tracked during the first ASTEX Lagrangian experiment, a shallow subtropical drizzling stratocumulus-capped marine boundary layer deepens after two days into a cumulus capped boundary layer with patchy stratocumulus. The models are forced with time varying boundary conditions at the sea-surface and the capping inversion to simulate the changing environment of the air column.The models all predict the observed deepening and decoupling of the boundary layer quite well, with cumulus cloud evolution and thinning of the overlying stratocumulus. Thus these models all appear capable of predicting transitions between cloud and boundary-layer types with some skill. The models also produce realistic drizzle rates, but there are substantial quantitative differences in the cloud cover and liquid water path between models. The differences between the eddy-resolving model results are nearly as large as between the single column model results. The eddy resolving models give a more detailed picture of the boundary-layer evolution than the single-column models, but are still sensitive to the choice of microphysical and radiative parameterizations, sub-grid-scale turbulence models, and probably model resolution and dimensionality. One important example of the differences seen in these parameterizations is the absorption of solar radiation in a specified cloud layer, which varied by a factor of four between the model radiation parameterizations.