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Branko Kosović and Judith A. Curry

Abstract

Using the large eddy simulation (LES) technique, the authors study a clear-air, stably stratified atmospheric boundary layer (ABL) as it approaches a quasi-steady state. The Beaufort Sea Arctic Stratus Experiment (BASE) dataset is used to impose initial and boundary conditions. The authors explore the parameter space of the boundary layer by varying latitude, surface cooling rate, geostrophic wind, inversion strength, and surface roughness. Recognizing the critical dependence of the results of LES on the subgrid-scale (SGS) model, they test and use a nonlinear SGS model, which is capable of reproducing the effects of backscatter of turbulent kinetic energy (TKE) and of the SGS anisotropies characteristic for shear-driven flows. In order to conduct a long-term LES so that an ABL can reach a quasi-steady state, a parallel computer code is developed and simulations with a spatial domain of up to 963 grid points are performed.

The authors analyze the evolution of the mean wind, potential temperature, and turbulence profiles as well as the turbulence budgets. In their simulations, they observe the development of features that are characteristic of a stably stratified ABL: a two-layer ABL structure, an elevated inversion, and an associated inversion wind maxima. Good agreement is found between the LES results and the observations and with Nieuwstadt’s analytical model. The authors study the dependence of the boundary layer height on the flow parameters and determine model coefficients for a truncated Zilitinkevich–Mironov model.

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Domingo Muñoz-Esparza and Branko Kosović

Abstract

Realistic multiscale simulations involve coupling of mesoscale and large-eddy simulation (LES) models, thus requiring efficient generation of turbulence in nested LES domains. Herein, we extend our previous work on the cell perturbation (CP) method to nonneutral atmospheric boundary layers (ABLs). A modified Richardson number scaling is proposed to determine the amplitude of the potential temperature perturbations in stable ABLs, with −1.0 overall providing optimum turbulence transition to a fully developed state (fetch reduced by a factor of 4–5, compared to the unperturbed cases). In the absence of perturbations, turbulence onset is triggered by a Kelvin–Helmholtz instability, typically occurring in the vicinity of the low-level jet maximum. It is found that a turbulent length scale can be used to more accurately estimate the optimum , where q is the turbulence kinetic energy, and N is the Brunt–Väisälä frequency. In convective ABLs, a perturbation amplitude based on mixed layer temperature variance scaling is proposed: . For that criterion to be optimum, the ratio , where is the wind speed at the top of the capping inversion, and is the convective velocity scale, needs to be incorporated: . This allows us to account for the competing roles of the surface thermal instability and the mean flow advection. For 10, the development fetch is reduced by a factor of 6, while when 3, the use of the CP method does not provide a significant advantage in the ability to generate turbulence, provided a smooth mesoscale inflow.

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Jeff Mirocha, Branko Kosović, and Gokhan Kirkil

Abstract

One-way concurrent nesting within the Weather Research and Forecasting Model (WRF) is examined for conducting large-eddy simulations (LES) nested within mesoscale simulations. Wind speed, spectra, and resolved turbulent stresses and turbulence kinetic energy from the nested LES are compared with data from nonnested simulations using periodic lateral boundary conditions. Six different subfilter-scale (SFS) stress models are evaluated using two different nesting strategies under geostrophically forced flow over both flat and hilly terrain. Neutral and weakly convective conditions are examined. For neutral flow over flat terrain, turbulence appears on the nested LES domains only when using the two dynamic SFS stress models. The addition of small hills and valleys (wavelengths of 2.4 km and maximum slopes of ± 10°) yields small improvements, with all six models producing some turbulence on nested domains. Weak convection (surface heat fluxes of 10 W m−2) further accelerates the development of turbulence on all nested domains. However, considerable differences in key parameters are observed between the nested LES domains and their nonnested counterparts. Nesting of a finer LES within a coarser LES provides superior results to using only one nested LES domain. Adding temperature and velocity perturbations near the inlet planes of nested domains shows promise as an easy-to-implement method to accelerate turbulence generation and improve its accuracy on nested domains.

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Fotini Katopodes Chow, Branko Kosović, and Stevens Chan

Abstract

The ability to determine the source of a contaminant plume in urban environments is crucial for emergency-response applications. Locating the source and determining its strength based on downwind concentration measurements, however, are complicated by the presence of buildings that can divert flow in unexpected directions. High-resolution flow simulations are now possible for predicting plume evolution in complex urban geometries, where contaminant dispersion is affected by the flow around individual buildings. Using Bayesian inference via stochastic sampling algorithms with a high-resolution computational fluid dynamics model, an atmospheric release event can be reconstructed to determine the plume source and release rate based on point measurements of concentration. Event-reconstruction algorithms are applied first for flow around a prototype isolated building (a cube) and then using observations and flow conditions from Oklahoma City, Oklahoma, during the Joint Urban 2003 field campaign. Stochastic sampling methods (Markov chain Monte Carlo) are used to extract likely source parameters, taking into consideration measurement and forward model errors. In all cases the steady-state flow field generated by a 3D Navier–Stokes finite-element code (FEM3MP) is used to drive thousands of forward-dispersion simulations. To enhance computational performance in the inversion procedure, a reusable database of dispersion simulation results is created. It is possible to successfully invert the dispersion problems to determine the source location and release rate to within narrow confidence intervals even with such complex geometries. The stochastic methodology here is general and can be used for time-varying release rates and reactive flow conditions. The results of inversion indicate the probability of a source being found at a particular location with a particular release rate, thus inherently reflecting uncertainty in observed data or the lack of enough data in the shape and size of the probability distribution. A composite plume showing concentrations at the desired confidence level can also be constructed using the realizations from the reconstructed probability distribution. This can be used by emergency responders as a tool to determine the likelihood of concentration at a particular location being above a threshold value.

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Domingo Muñoz-Esparza, Jeremy A. Sauer, Rodman R. Linn, and Branko Kosović

Abstract

Mesoscale models are considered to be the state of the art in modeling mountain-wave flows. Herein, the authors investigate the role and accuracy of planetary boundary layer (PBL) parameterizations in handling the interaction between large-scale mountain waves and the atmospheric boundary layer. To that end, recent large-eddy simulation (LES) results of mountain waves over a symmetric two-dimensional bell-shaped hill are used and compared to four commonly used PBL schemes. It is found that one-dimensional PBL parameterizations produce reasonable agreement with the LES results in terms of vertical wavelength, amplitude of velocity, and turbulent kinetic energy distribution in the downhill shooting-flow region. However, the assumption of horizontal homogeneity in PBL parameterizations does not hold in the context of these complex flow configurations. This inappropriate modeling assumption results in a vertical wavelength shift, producing errors of approximately 10 m s−1 at downstream locations because of the presence of a coherent trapped lee wave that does not mix with the atmospheric boundary layer. In contrast, horizontally integrated momentum flux derived from these PBL schemes displays a realistic pattern. Therefore, results from mesoscale models using ensembles of one-dimensional PBL schemes can still potentially be used to parameterize drag effects in general circulation models. Nonetheless, three-dimensional PBL schemes must be developed in order for mesoscale models to accurately represent complex terrain and other types of flows where one-dimensional PBL assumptions are violated.

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Gokhan Kirkil, Jeff Mirocha, Elie Bou-Zeid, Fotini Katopodes Chow, and Branko Kosović

Abstract

The performance of a range of simple to moderately-complex subfilter-scale (SFS) stress models implemented in the Weather Research and Forecasting (WRF) model is evaluated in large-eddy simulations of neutral atmospheric boundary layer flow over both a flat terrain and a two-dimensional symmetrical transverse ridge. Two recently developed dynamic SFS stress models, the Lagrangian-averaged scale-dependent (LASD) dynamic model and the dynamic reconstruction model (DRM), are compared with the WRF model’s existing constant-coefficient linear eddy-viscosity and (as of version 3.2) nonlinear SFS stress models to evaluate the benefits of more sophisticated and accurate, but also more computationally expensive approaches.

Simulation results using the different SFS stress models are compared among each other, as well as against the Monin–Obukhov similarity theory. For the flat terrain case, vertical profiles of mean wind speed from the newly implemented dynamic models show the best agreement with the similarity solution, improving even upon the nonlinear model, which likewise yields a significant improvement compared to the Smagorinsky model. The more sophisticated SFS stress models more successfully predict the expected production and inertial range scaling of power spectra, especially near the surface, with the dynamic models achieving the best scaling overall. For the transverse ridge case, the nonlinear model predicts the greatest amount of reverse flow in the lee of the ridge, and also demonstrates the greatest ability to duplicate qualitative features of the highest-resolution simulations at coarser resolutions. The dynamic models’ flow distributions in the lee of the ridge did not differ significantly from the constant-coefficient Smagorinsky model.

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Masih Eghdami, Ana P. Barros, Pedro A. Jiménez, Timothy W. Juliano, and Branko Kosovic

Abstract

Accurate representation of heterogeneous surface layer processes is essential for numerical weather prediction (NWP) with sub-kilometer grid spacing. NWP models such as the Weather Research and Forecasting (WRF) Model generally use second-moment turbulent models for parameterizing the planetary boundary layer (PBL). The most common parameterizations follow Mellor–Yamada and account for the vertical turbulent mixing only; that is, standard PBL parameterizations are one-dimensional (1DPBL). The horizontal diffusion of momentum is parameterized based on Smagorinsky’s model for numerical stability. Although the combination of 1DPBL and 2D Smagorinsky parameterizations is successful at coarse grid resolutions (e.g., grid-size dx ∼ 12–2 km), it does not represent well the effect of horizontal turbulence as gridcell size decreases (<1 km). To reconcile the representation of vertical and horizontal turbulent mixing, a full three-dimensional PBL scheme (3DPBL) based on the Mellor–Yamada model was implemented in WRF. The 3DPBL uses the horizontal and vertical turbulent fluxes diagnosed from the flow gradients to handle the turbulent mixing. These gradients cannot be directly calculated near the surface. Therefore, the 3DPBL parameterization is coupled herein to a second-order diagnostic model of the three-dimensional turbulent fluxes in the surface layer. Several adjustments to the original Mellor–Yamada model, including a modified length scale, were introduced to capture flow anisotropy and dependence on stability conditions. The results are compared against data from the Wind Forecast Improvement Project 2 (WFIP2) for different weather regimes and using different grid resolutions to examine stability and scale dependency.

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Jeff Mirocha, Gokhan Kirkil, Elie Bou-Zeid, Fotini Katopodes Chow, and Branko Kosović

Abstract

The Weather Research and Forecasting Model permits finescale large-eddy simulations (LES) to be nested within coarser simulations, an approach that can generate more accurate turbulence statistics and improve other aspects of simulated flows. However, errors are introduced into the finer domain from the nesting methodology. Comparing nested domain, flat-terrain simulations of the neutral atmospheric boundary layer with single-domain simulations using the same mesh, but instead using periodic lateral boundary conditions, reveals the errors contributed to the nested solution from the parent domain and nest interfaces. Comparison of velocity spectra shows good agreement among higher frequencies, but greater power predicted on the nested domain at lower frequencies. Profiles of mean wind speed show significant near-surface deficits near the inflow boundaries, but equilibrate to improved values with distance. Profiles of the vertical flux of x momentum show significant underprediction by the nested domain close to the surface and near the inlet boundaries. While these underpredictions of the stresses, which cause the near-surface velocity deficits, attenuate with distance within the nested domains, significant errors remain throughout. Profiles of the resolved turbulence kinetic energy show considerable deviations from their single-domain values throughout the nested domains. The authors examine the accuracy of these parameters and their sensitivities to the turbulence subfilter stress model, mesh resolution, and grid aspect ratio, and provide guidance to practitioners of nested LES.

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Paul E. Bieringer, Steven Hanna, George Young, Branko Kosovic, John Hannan, and Ryohji Ohba
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Timothy W. Juliano, Branko Kosović, Pedro A. Jiménez, Masih Eghdami, Sue Ellen Haupt, and Alberto Martilli

Abstract

Generating accurate weather forecasts of planetary boundary layer (PBL) properties is challenging in many geographical regions, oftentimes due to complex topography or horizontal variability in, for example, land characteristics. While recent advances in high-performance computing platforms have led to an increase in the spatial resolution of numerical weather prediction (NWP) models, the horizontal gridcell spacing (Δx) of many regional-scale NWP models currently fall within or are beginning to approach the gray zone (i.e., Δx ≈ 100–1000 m). At these gridcell spacings, three-dimensional (3D) effects are important, as the most energetic turbulent eddies are neither fully parameterized (as in traditional mesoscale simulations) nor fully resolved [as in traditional large-eddy simulations (LES)]. In light of this modeling challenge, we have implemented a 3D PBL parameterization for high-resolution mesoscale simulations using the Weather Research and Forecasting Model. The PBL scheme, which is based on the algebraic model developed by Mellor and Yamada, accounts for the 3D effects of turbulence by calculating explicitly the momentum, heat, and moisture flux divergences in addition to the turbulent kinetic energy. In this study, we present results from idealized simulations in the gray zone that illustrate the benefit of using a fully consistent turbulence closure framework under convective conditions. While the 3D PBL scheme reproduces the evolution of convective features more appropriately than the traditional 1D PBL scheme, we highlight the need to improve the turbulent length scale formulation.

Significance Statement

The spatial resolution of weather models continues to increase at a rapid rate in accordance with the enhancement of computing power. As a result, smaller-scale atmospheric features become more explicitly resolved. However, most numerical models still ignore the impact of horizontal weather variations on boundary layer flows, which becomes more important at these smaller spatial scales. To address this issue, we have implemented a new modeling approach, using fundamental principles, which accounts for horizontal variability. Our results show that including three-dimensional effects of turbulence is necessary to achieve realistic boundary layer characteristics. This novel technique may be useful for many applications including complex terrain flows, pollutant dispersion, and surface–atmosphere interaction studies.

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