1. Introduction
Atmospheric models supporting local mesh refinement are frequently used to downscale coarse-resolution simulations. Downscaling within the mesoscale realm has been shown to produce more accurate and higher-fidelity results (e.g., Caldwell et al. 2009; Liu et al. 2011), by incorporating higher-resolution land surface data and resolving smaller scales of atmospheric motion, the effects of which must otherwise be parameterized. Based on these successes, downscaling is increasingly being extended to resolutions permitting the large-eddy simulation (LES) approach, whereby the three-dimensional turbulence providing energy to the classical inertial subrange is explicitly resolved. Such an approach can potentially reduce errors from mesoscale planetary boundary layer (PBL) parameterizations, most of which are based on the assumption of boundary layer homogeneity over a grid cell, and therefore implicitly not designed for use at very high resolutions. High-resolution simulations involving heterogeneous terrain or forcing require LES, which explicitly resolves the scales of motion responsible for most of the stress and turbulent kinetic energy (TKE). Such high-resolution simulations are essential for many applications, including for example, transport and dispersion, wind resource characterization, and wind turbine siting.
Atmospheric models such as the Weather Research and Forecasting Model (WRF; Skamarock et al. 2008) permit downscaling via grid nesting, wherein the lateral boundary conditions for a nested domain are provided by the bounding simulation. Nests can be implemented within one another to achieve stepwise reductions in mesh spacing, permitting both large scales of weather and finer mesoscale features to influence the LES nested within. This approach can potentially provide the LES with more realistic atmospheric forcing than is traditionally obtained via offline coupling between mesoscale and LES models (e.g., Zajaczkowski et al. 2011). Nesting within the same code also eliminates inconsistencies between the grid structures, physical process models, and numerical solution methods encountered when coupling different models. In addition to one-way nesting, for which the bounding domain receives no feedback from the nested domain, WRF also facilitates two-way nesting, whereby information from the nested domain influences the bounding simulation. While two-way nesting is needed when effects resolved on a finer resolution nest are required by the solution on the bounding domain, many ABL and microscale applications simply require downscaling, where accurate large-scale forcing is essential, and for which one-way nesting is sufficient. We focus on one-way nesting herein.
While mechanisms for downscaling from mesoscale to LES exist in WRF (and other models), the extant methodology is constrained by shortcomings of current parameterizations and approaches. Wyngaard (2004) details challenges to developing closure models for unresolved turbulence effects in the terra incognita, a range of scales between traditional mesoscale (greater than 1 km) and LES (order of 1 km or less). Mirocha et al. (2013) and Moeng et al. (2007) describe difficulties involved in nesting finely resolved LES within a coarser-resolution LES within WRF, for which adequate closure models exist, yet for which errors are introduced into the nested LES solution via the nesting procedure. Moeng et al. (2007) were able to recover reasonable LES performance in nested LES under moderately strong forcing, but only after modifying the subfilter turbulence model, and using nested domains of sufficient sizes. Mirocha et al. (2013) investigated neutral flow over flat terrain and showed large departures in mean wind speed, stress, and resolved TKE within the nested LES, relative to single-domain simulations conducted on identical meshes, but instead using periodic lateral boundary conditions. These errors gradually attenuated with distance within the nested domains, yet often remained large, even several kilometers (several hundred grid cells) downstream. Additional problems related to both mesh refinement (e.g., Vanella et al. 2008; Piomelli et al. 2006) and the instigation of turbulence at laminar inflow boundaries for LES (e.g., Keating et al. 2004) have been identified.
Despite these caveats, downscaling from mesoscale to LES is increasingly being employed in an attempt to improve the fidelity and realism of atmospheric simulations. Unfortunately, little information exists regarding conditions under which the approach is appropriate, and what the potential errors might be. This study extends the work of Mirocha et al. (2013) to the nesting of LES within mesoscale flows, for which the inflow contains essentially no resolved turbulence. Many practitioners of downscaling expect that turbulence will spontaneously develop within a short distance from the inflow boundaries to nested LES domains due to the reduced mesh spacing. We investigate the veracity of this assumption under three forcing scenarios: neutral and weakly convective flow over flat terrain, and neutral flow over hilly terrain. We evaluate six different subfilter-scale (SFS) stress modeling approaches, and two different nesting methodologies. We also examine the addition of perturbations to the potential temperature and velocity fields near the inflow boundaries of nested domains as a simple-to-implement method to improve turbulence generation and flow characteristics downstream. The goal of this study is to inform WRF users of current limitations, provide the best practices, and to elucidate fruitful areas for future research.
2. Methodology
This study examines the accuracy of low-order statistics obtained from LES nested within mesoscale simulations using WRF. The base simulation is neutral flow over flat terrain, using a roughness length of 
The accuracies of turbulence parameters produced within the nested LES are evaluated by comparison with stand-alone (nonnested) LES. The stand-alone LES use computational meshes that are identical to those of the nested LES, and use the same large-scale forcing, but instead utilize periodic lateral boundary conditions directly, providing the stand-alone LES with essentially unlimited fetches upon which turbulence can develop to statistically steady behavior. Rather than evaluating the accuracies of the SFS stress models themselves (as done previously, see Mirocha et al. 2010; Kirkil et al. 2012), here we take the stand-alone solutions as the “truth,” for each SFS stress model, and examine the development of flow and turbulence characteristics within the nested LES domains relative to the stand-alone solutions.
Two LES domains are nested within the mesoscale domain, as depicted in Fig. 1. The larger nested domain is a coarse LES, using 
Computational environment. Large and small white rectangles show coarse and fine nested LES domain locations, respectively, within the mesoscale domain. Background shows sinusoidal hills (light) and valleys (dark) used in undulating terrain simulations; otherwise, the terrain is flat. The thin white line shows P65, the location 65% of the distance across the fine LES domain, from left to right, from which various parameters are evaluated.
Citation: Monthly Weather Review 142, 2; 10.1175/MWR-D-13-00064.1
The heights of WRF’s pressure-based vertical coordinate levels were specified from prescribed 
Physical and computational dimensions of simulation domains, where nx, ny, and nz are the number of grid points in the x, y, and z directions, respectively; 
As the primary focus of this study is the development of resolved turbulence on nested LES domains under the challenging conditions of weak forcing, three scenarios are investigated: neutral flow over flat terrain, as described above; neutral flow over sinusoidal hills and valleys, with wavelengths of 2.4 km in each direction and maximum slopes of 
a. Modeling of subfilter-scale fluxes in LES
We examine six different approaches to modeling the SFS stresses and fluxes. The simplest are two linear constant-coefficient eddy viscosity models. The Smagorinsky model (SMAG; Smagorinsky 1963; Lilly 1967) uses the strain rate, a length scale based upon the local grid spacing, and one coefficient. The TKE model, similarly based, also uses SFS TKE, obtained from an additional equation. The Nonlinear Backscatter and Anisotropy models (NBA1 and NBA2; Kosović 1997) include additional nonlinear terms consisting of products of the strain and rotation rate tensors. The NBA2 model incorporates SFS TKE from the TKE model’s SFS TKE equation. As the NBA models only provide momentum fluxes, scalar fluxes are obtained from the SMAG (NBA1) or TKE (NBA2) models.
The above four SFS stress models are contained in the current WRF release (as of version 3). We also examine two dynamic models not in the current release. These models utilize explicit spatial filters to obtain spatially and temporally varying values of the coefficient used in the SMAG closure. The Lagrangian-Averaged Scale-Dependent (LASD; Bou-Zeid et al. 2005, 2008) model uses two spatial filters to extrapolate the value of the coefficient used for the SFS stresses from resolved stresses at two scales. The coefficients are stabilized by averaging along fluid pathlines. The Dynamic Reconstruction Model (DRM; Chow et al. 2005) uses a scale-invariant dynamic approach based on one level of filtering to obtain the coefficient. The scale-similarity term is obtained using explicit filtering and reconstruction, which provides variable orders of reconstruction. In this study we use the lowest order, level 0 (DRM0).
b. Surface boundary conditions
c. Model initialization and solution procedure
All simulations were initialized dry, and no cloud, radiation, or land surface models were used. The initial profile of the resolved 
3. Results
Results are examined after 12 h of simulated time, permitting the mesoscale inflows to the LES domains to approach equilibrium with the forcing. The coarse and fine nested LES domains were initiated at hours 8 and 10, respectively. The stand-alone LES were run for 8 h using the LASD model, after which simulations were continued further using each of the SFS stress models.
a. Neutral flow over flat terrain
Figure 2 shows instantaneous contours of the wind speed at the beginning of hour 12, from simulations on each LES domain, from each SFS model, at approximately 
Instantaneous contours of 
Citation: Monthly Weather Review 142, 2; 10.1175/MWR-D-13-00064.1
The largest panels show the coarse LES domains (CN), which are nested within the mesoscale domain (M, not shown). The smaller panels show two different nesting strategies for the fine nested LES, the top panel showing two levels of nesting (F2N), with the fine LES nested within the coarse nested LES, and the bottom panel showing the fine LES nested directly within M (F1N). The locations of the nested LES domains are indicated by the dotted rectangles in the larger panels (also by the smaller white rectangle in Fig. 1).
The bottom panels show results from stand-alone (SA) coarse (CSA) and fine (FSA) LES, which use periodic boundary conditions directly, as described in section 2. Only results using the LASD model are shown here, for qualitative comparison. The other models’ SA solutions are used in analyses described below.
Figure 2 shows that turbulence develops differently on the nested domains depending upon the SFS stress model. While each model produces turbulent flow on its corresponding CSA and FSA domains (only LASD is shown here), only the dynamic models (DRM0 and LASD) generate turbulence on any of the nested LES domains. Turbulence gradually forms on CN, before flowing into the fine LES nested within (F2N). Nesting the fine LES directly within the mesoscale domain does not yield turbulence on the fine LES domain (F1N) until a significant distance from the inflow boundaries, suggesting the utility of an intermediate coarse LES upon which turbulence can begin to form and further develop within a the finer LES. The triangular structures appearing in each nested domains are numerical artifacts of the nesting procedure that have no discernible influence once the flow becomes turbulent.
The accuracy of the turbulence appearing on the dynamic models’ CN and F2N domains is evaluated using velocity spectra, resolved turbulence kinetic energy 
For the nested LES domains, the 
The resolved turbulence kinetic energy is defined as 
Figure 3 shows the three turbulence parameters from simulations using the two dynamic SFS stress models (LASD and DRM0), indicating the nested LES values at the 
Flow parameters from neutral flat terrain simulations using the DRM0 and LASD SFS stress models. (left two columns) Spectra of 
Citation: Monthly Weather Review 142, 2; 10.1175/MWR-D-13-00064.1
Thick gray lines in Figs. 3a1,a2, and Figs. 3b1,b2 show spectra from the FSA and CSA domains, with thin black lines showing corresponding spectra from the nested LES domains, CN and F2N. Thin gray straight lines show the expected −2/3 slope within the inertial subrange for compensated spectra. Figures 3a3,a4, and Figs. 3b3,b4 show profiles of 
Among the two SFS models, the LASD simulation produces more rapid spectral development and better agreement between the nested and SA domains at P65. The DRM0 spectra are not well developed by the time the flow reaches P65 on CN; however, the spectra do develop fully within F2N, although power is under (over) predicted at lower (higher) frequencies. The LASD spectra show better agreement between CN and CSA than between F2N and FSA, with slightly overpredicted power on F2N.
Profiles of 
The disparate behaviors of the models’ F2N 
Figure 4 shows profiles of wind speed 
(a)–(f) Profiles of 
Citation: Monthly Weather Review 142, 2; 10.1175/MWR-D-13-00064.1
b. Neutral flow over hilly terrain
Neutral flow over flat terrain is challenging for nested simulations as, absent instabilities or surface features to distort the flow, turbulence must form from small inhomogeneities, a slow process. We investigate the effects of undulating terrain on turbulence formation, using small sinusoidal hills and valleys, with wavelengths of 2.4 km (as shown in Fig. 1) and maximum slopes of 
Figure 5 shows contours of 
Instantaneous contours of 
Citation: Monthly Weather Review 142, 2; 10.1175/MWR-D-13-00064.1
Figures 6 and 7 show spectra and profiles of 
Flow parameters from neutral undulating terrain simulations using all six SFS stress models. (left two columns) Spectra of 
Citation: Monthly Weather Review 142, 2; 10.1175/MWR-D-13-00064.1
Flow parameters from neutral undulating terrain simulations using all six SFS stress models. (left two columns) Spectra of 
Citation: Monthly Weather Review 142, 2; 10.1175/MWR-D-13-00064.1
Figure 6 shows spectra and profiles at P65, which is aligned with the peaks and valleys of the undulations in the 
While the spectra on FSA and F2N appear similar for all simulations, larger differences are observed on CN, with only the dynamic models producing smooth distributions at higher wavenumbers on CN. The NBA models show the slowest development of turbulence spectra on CN. The NBA2 model was unstable for this case using the default value of 
The SMAG, TKE, and NBA models generally underpredict 
c. Weakly convective flow over flat terrain
We investigate the influence of weak convective instability by adding a small surface heat flux of 
Instantaneous contours of 
Citation: Monthly Weather Review 142, 2; 10.1175/MWR-D-13-00064.1
Figure 9 shows spectra, 
Flow parameters from weakly convective flat terrain simulations using all six SFS stress models. (left two columns) Spectra of 
Citation: Monthly Weather Review 142, 2; 10.1175/MWR-D-13-00064.1
4. Addition of perturbations near nest inflow planes
In the absence of strong forcing, turbulence generation from nonturbulent, mesoscale inflow is slow, requiring a large upwind fetch to generate turbulence at an area of interest (e.g., P65). Various methods to accelerate turbulence development exist; however, no consensus on the best practice has emerged. The addition of random perturbations (e.g., Keating et al. 2004) is the simplest method; however, the length scale of turbulence generation is typically large. Perturbation recycling and rescaling methods (e.g., Lund et al. 1998) are more efficient; however, those methods are based upon equilibrium assumptions, and require information from within the LES domain, hence, they are of limited applicability to real nested LES setups. Precursor simulations (e.g., Thomas and Williams 1999), which use a separate LES to develop turbulence, can provide more accurate turbulent inflow; however, significant additional computation is required, and the precursor domain may not reflect the upwind fetch in a real nested LES setup.
Given the absence of a consensus on the best approach and the unique requirements of using realistic mesoscale inflow to drive LES nested within, we investigate an approach that is general and simple to implement. Tendencies are added to WRF’s 
Figure 10 shows the spatial pattern of the perturbation tendencies, with light and dark indicating positive and negative values. The top and bottom panels show 
Spatial pattern of perturbation tendencies added to 
Citation: Monthly Weather Review 142, 2; 10.1175/MWR-D-13-00064.1
a. Neutral flow over flat terrain
The search for optimal perturbations was limited, the goal being examination of the viability of the basic approach. Amplitudes of 
1) Perturbations using the LASD model
As the LASD model provided the best overall performance on nested domains, we use it to examine four perturbation strategies. We begin with neutral flow over flat terrain. Figure 11 shows spectra and 
Flow parameters from neutral flat terrain simulations using the LASD SFS stress model, showing the impact of adding perturbations with spatial extents of 24 (P24) and 8 (P8) grid points in each horizontal direction, as shown in Fig. 10, (far left panels) to the coarse nested LES (CN) and fine LES nested within CN (F2N), respectively. (left two columns) Spectra of 
Citation: Monthly Weather Review 142, 2; 10.1175/MWR-D-13-00064.1
While Fig. 11 shows profiles at one location within F2N, these quantities change as the flow traverses the extent of the F2N domain. Figure 12 shows values of 
(a) 
Citation: Monthly Weather Review 142, 2; 10.1175/MWR-D-13-00064.1
Consistent with the profiles at P65 shown in Fig. 11, the simulations not using perturbations on CN most strongly overpredict 
We hypothesize that the disparate effects of perturbations of different sizes on F2N are related to their impacts on the cascade process. Assuming an effective mesh resolution of 
The overpredictions of 
The perturbations influence 
Of the simulations using perturbations on CN, those that also use the large perturbations on F2N (P24 CN, P24 F2N) create the largest overpredictions of 
Adding smaller period 8 perturbations on F2N (P24 CN, P8 F2N) has a muted effect compared to the P24 CN case, slightly accelerating the rate of increase of 
2) Perturbations using all six SFS stress models
As perturbations of period 24 on CN and 8 on F2N produced among the best overall results using the LASD model, these perturbations were applied using all six SFS stress models. Figure 13 shows instantaneous 
Instantaneous contours of 
Citation: Monthly Weather Review 142, 2; 10.1175/MWR-D-13-00064.1
Figure 14 shows the results of perturbations on spectra and 
Flow parameters from neutral flat terrain simulations using all six SFS stress models, using perturbations with spatial extents of 24 grid points in each horizontal direction on the coarse nested LES (CN), and 8 grid points on fine LES nested within CN (F2N), respectively. (left two columns) Spectra of 
Citation: Monthly Weather Review 142, 2; 10.1175/MWR-D-13-00064.1
While the LASD model shows good agreement between the F2N and FSA profiles at P65, other models show larger discrepancies. Period 24 perturbations were applied to only the CN domains using the other models (not shown); however, results were worse overall than when perturbations were used on both domains, except for DRM0, which performed slightly better. Adding period 8 perturbations to F2N greatly reduces the overpredictions of 
b. Neutral flow over hilly terrain
Figures 15 and 16 show the results of adding perturbations of period 24 on CN and period 8 on F2N to the hilly terrain simulations. Comparison with the nonperturbed simulations (Figs. 6 and 7) shows generally improved agreement between the F2N and FSA spectra and profiles, even as the spectra on CN develop more slowly.
Flow parameters from neutral undulating terrain simulations using all six SFS stress models, using perturbations with spatial extents of 24 grid points in each horizontal direction on the coarse nested LES (CN), and 8 grid points on fine LES nested within CN (F2N), respectively. (left two columns) Spectra of 
Citation: Monthly Weather Review 142, 2; 10.1175/MWR-D-13-00064.1
Flow parameters from neutral flow over undulating terrain simulations using all six SFS stress models, using perturbations with spatial extents of 24 grid points in each horizontal direction on the coarse nested LES (CN), and 8 grid points on fine LES nested within CN (F2N), respectively. (left two columns) Spectra of 
Citation: Monthly Weather Review 142, 2; 10.1175/MWR-D-13-00064.1
c. Weakly convective flow over flat terrain
Figure 17 shows results from the weakly convective simulations using perturbations of period 24 on CN and period 8 on F2N. Comparison with the nonperturbed simulation (Fig. 9) shows either improvement or degradation, depending upon the model. While the SMAG, TKE, and NBA simulations show improved 
Flow parameters from weakly convective flat terrain simulations using all six SFS stress models, using perturbations with spatial extents of 24 grid points in each horizontal direction on the coarse nested LES (CN), and 8 grid points on fine LES nested within CN (F2N), respectively. (left two columns) Spectra of 
Citation: Monthly Weather Review 142, 2; 10.1175/MWR-D-13-00064.1
5. Summary and conclusions
Under the relatively weak forcing conditions examined herein, nesting from a mesoscale simulation down to LES using WRF’s extant nesting strategy did not reliably produce turbulence fields that resembled those from stand-alone LES using periodic lateral boundary conditions. For neutral flow over flat terrain, while all six SFS stress models produced realistic turbulence on stand-alone (periodic) domains, only the two dynamic models (LASD and DRM0) produced turbulence on nested LES domains. Adding small terrain features (wavelengths of 2.4 km and maximum slopes of 10°) accelerated turbulence formation, resulting in some turbulence on nested LES domains using all six models. However, the 
The dynamic models, by locally reducing dissipation rates, allowed turbulence to develop most rapidly, producing superior performance on nested domains. Other models contain parameters that could potentially be modified to accelerate turbulence formation.
Adding small thermal and velocity perturbations near the inflow boundaries of nested LES domains accelerated turbulence formation and improved nested LES results, except for the dynamic models under weakly convective condition, which produced good results without perturbations. For the coarse LES nested within the mesoscale simulations, perturbations with periods of 24 grid cells produced the best results among those investigated. For fine LES nested within coarse LES, smaller perturbations (periods of 8 grid cells) were superior, by seeding scales near the inertial subrange of the larger eddies advecting in from the bounding domain, accelerating the downscale energy cascade.
Nesting a fine LES domain within a coarser surrounding LES, upon which turbulence can begin to develop, was found superior to nesting it directly within the mesoscale simulation, irrespective of perturbation approaches applied.
Considerable differences were observed in the effects of perturbations on the various SFS stress models. Each model likely possesses a unique optimal perturbation approach. The effects of perturbations vary with stability, affording generally greater benefits during neutral than convective conditions. Real atmospheric flows are seldom neutral; however, they are often weakly stable and still turbulent, a context for which perturbations would be expected to have similar results to the neutral cases examined herein. While our initial results are encouraging, further exploration of these issues is needed to establish a robust framework for downscaling mesoscale flows to LES under variable forcing conditions using WRF.
Acknowledgments
We thank Tina Chow and Elie Bou-Zeid for many helpful discussions. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344, and was supported by both the Laboratory Directed Research and Development program, and the U.S. DOE Office of Energy Efficiency and Renewable Energy.
APPENDIX
Details of SFS Stress Model Formulations
a. Constant-coefficient Smagorinsky model (SMAG)
b. 1.5-order TKE model (TKE)
c. Lagrangian-averaged scale dependent model (LASD)
The LASD model (Bou-Zeid et al. 2005, 2008) is based upon Eqs. (A1) and (A2), with 
The LASD model is stabilized via Lagrangian averaging, using weighted time histories for averaged quantities along fluid path lines.
Scalar fluxes for the LASD model are computed from Eq. (A3).
d. Nonlinear backscatter and anisotropy models (NBA1 and NBA2)
e. Dynamic reconstruction model (DRM)
The DRM (Chow et al. 2005) is a mixed model, utilizing both an eddy-viscosity and a scale-similarity term. The eddy viscosity term is obtained following the scale-invariant dynamic formulation of Wong and Lilly (1994). The scale-similarity term is computed using explicit filtering and reconstruction of the resolvable subfilter-scale (RSFS) stresses. These are obtained by first reconstructing the “unfiltered” velocities, accomplished by applying the inverse of the explicit spatial filter to the (filtered) prognostic velocities. A series approximation is used for the inverse filter operation, for which the number of terms retained in the series determines the order of reconstruction. Next, Eq. (2) is used to compute the RSFS stresses by substituting the unfiltered velocities into 
For the DRM scalar fluxes, the eddy viscosity component is computed from Eq. (A3) using 
f. Near wall stress augmentation for dynamic models
REFERENCES
Arya, S. P., 2001: Introduction to Micrometeorology. 2nd ed. Academic Press, 420 pp.
Bou-Zeid, E., C. Meneveau, and M. B. Parlange, 2005: A scale-dependent Lagrangian dynamic model for large eddy simulation of complex turbulent flows. Phys. Fluids, 17, 025105, doi:10.1063/1.1839152.
Bou-Zeid, E., N. Vercauteren, M. B. Parlange, and C. Meneveau, 2008: Scale dependence of subgrid-scale model coefficients: An a priori study. Phys. Fluids, 20, 115106, doi:10.1063/1.2992192.
Brown, A. R., J. M. Hobson, and N. Wood, 2001: Large-eddy simulation of neutral turbulent flow over rough sinusoidal ridges. Bound.-Layer Meteor., 98, 411–441.
Caldwell, P., H.-N. S. Chin, D. C. Bader, and G. Bala, 2009: Evaluation of a WRF dynamical downscaling simulation over California. Climatic Change, 95, 499–521.
Chow, F. K., 2004: Subfilter-scale turbulence modeling for large eddy simulation of the atmospheric boundary layer over complex terrain. Ph.D. dissertation, Stanford University, 339 pp.
Chow, F. K., R. L. Street, M. Xue, and J. H. Ferziger, 2005: Explicit filtering and reconstruction turbulence modeling for large-eddy simulation of neutral boundary layer flow. J. Atmos. Sci., 62, 2058–2077.
Deardorff, J. W., 1972: Numerical investigation of neutral and unstable planetary boundary layers. J. Atmos. Sci., 29, 91–115.
Holton, J. R., 1992: An Introduction to Dynamic Meteorology. 3rd ed. Academic Press, 511 pp.
Keating, A., U. Piomelli, E. Balaras, and H.-J. Kaltenbach, 2004: A priori and a posteriori tests of inflow conditions for large-eddy simulation. Phys. Fluids, 16, 4696–4712.
Kirkil, G., J. D. Mirocha, F. K. Chow, and E. Bou-Zeid, 2012: Implementation and evaluation of dynamic subfilter-scale stress models for large-eddy simulation using WRF. Mon. Wea. Rev., 140, 266–284.
Kosović, B., 1997: Subgrid-scale modeling for the large-eddy simulation of high-Reynolds-number boundary layers. J. Fluid Mech., 336, 151–182.
Lilly, D. K., 1967: The representation of small-scale turbulence in numerical experiment. Proc. IBM Scientific Computing Symp. on Environmental Sciences, White Plains, NY, IBM, 195–210.
Liu, Y., and Coauthors, 2011: Simultaneous nested modeling from the synoptic scale to the LES scale for wind energy applications. J. Wind Eng. Ind. Aerodyn., 99, 308–319.
Lund, T., X. Wu, and D. Squires, 1998: Generation of turbulent inflow data for spatially developing boundary layer simulation. J. Comput. Phys., 140, 233–258.
Mirocha, J. D., J. K. Lundquist, and B. Kosović, 2010: Implementation of a nonlinear subfilter turbulence stress model for large-eddy simulation in the Advanced Research WRF model. Mon. Wea. Rev., 138, 4212–4228.
Mirocha, J. D., G. Kirkil, E. Bou-Zeid, F. K. Chow, and B. Kosović, 2013: Transition and equilibration of neutral atmospheric boundary layer flow in one-way nested large eddy simulations using the Weather Research and Forecasting Model. Mon. Wea. Rev., 141, 918–940.
Moeng, C.-H., J. Dudhia, J. B. Klemp, and P. P. Sullivan, 2007: Examining two-way nesting for large eddy simulation of the PBL using the WRF model. Mon. Wea. Rev., 135, 2295–2311.
Muñoz-Esparza, D., B. Cañadillas, T. Neumann, and J. van Beeck, 2012: Turbulent fluxes, stability and shear in the offshore environment: Mesoscale modelling and field observations at FINO1. J. Renewable Sustainable Energy,4, 063136, doi:10.1063/1.4769201.
Nakanishi, M., and H. Niino, 2004: An improved Mellor–Yamada level-3 model with condensation physics: Its design and verification. Bound.-Layer Meteor., 112, 1–31.
Piomelli, U., S. Kang, F. Ham, and G. Iaccarino, 2006: Effect of discontinuous filter width in large-eddy simulations of plane channel flow. Studying Turbulence Using Numerical Simulation Database—XI, Proceedings of the Summer Program 2006, Center for Turbulence Research, 151–162. [Available online at http://ctr.stanford.edu/ctrsp06/piomelli.pdf.]
Skamarock, W. C., 2004: Evaluating mesoscale NWP models using kinetic energy spectra. Mon. Wea. Rev., 132, 3019–3032.
Skamarock, W. C., and Coauthors, 2008: A description of the advanced research WRF version 3. NCARTech. Note NCAR/TN-4751-STR, National Center for Atmospheric Research, 88 pp.
Smagorinsky, J., 1963: General circulation experiments with the primitive equations. Mon. Wea. Rev., 91, 99–152.
Thomas, T. G., and J. J. R. Williams, 1999: Simulation of skewed turbulent flow past a surface mounted cube. J. Wind Eng. Ind. Aerodyn., 81, 347–360.
Vanella, M., U. Piomelli, and E. Balaras, 2008: Effect of grid discontinuities on large-eddy simulation statistics and flow fields. J. Turbul., 9, 1–23.
Wong, V. C., and D. K. Lilly, 1994: A comparison of two dynamic subgrid closure methods for turbulent thermal-convection. Phys. Fluids, 6, 1016–1023.
Wyngaard, J. C., 2004: Toward numerical modeling in the “Terra Incognita.” J. Atmos. Sci., 61, 1816–1826.
Zajaczkowski, F. J., S. E. Haupt, and K. J. Schmehl, 2011: A preliminary study of assimilating numerical weather prediction data into computational fluid dynamics models for wind prediction. J. Wind Eng. Ind. Aerodyn., 99, 320–329, doi:10.1016/j.jweia.2011.01.023.
The tendencies for WRF’s prognostic variables are multiplied by column mass (in units of Pa).