We investigate the ability of the Weather Research and Forecasting model to perform large-eddy simulation of canonical flows. This is achieved through comparison of the simulation outputs with measurements from sonic anemometers on a 250 m meteorological mast located at Østerild, in northern Denmark. Østerild is on a flat and rough area, and for the predominant wind directions, the atmospheric flow can be considered to be close to homogeneous. The idealized simulated flows aim at representing atmospheric boundary layer turbulence under unstable, neutral, and stable stability conditions at the surface, which are statistically significant conditions observed at Østerild. We found that the resolved fields from the simulations appear to have the characteristics of the three stability regimes. Vertical profiles of observed mean wind speeds and direction are well reproduced by the simulations, with the largest differences under near-neutral conditions, where the effect of the subgrid-scale model is evident on the vertical wind shear close to the surface. Vertical profiles of observed eddy fluxes are also well reproduced by the simulations, with the largest differences for the three velocity component variances under stable stability conditions, although nearly always within the observed variability. With regards to turbulent kinetic energy, we find good agreement between observations and simulations at all vertical levels. Simulated and observed velocity spectra match very well and show very similar behavior with height and with atmospheric stability within the low-frequency interval; at the effective resolution, the simulated spectra show the typical drop-off of finite differences. Our findings demonstrate that these idealized simulations reproduce the characteristics of atmospheric stability regimes often observed at a high turbulent and flat site within a direction sector, where the air flows over nearly homogeneous land.

For many applications and, in particular, for wind energy, we would like to characterize the long-term site conditions, i.e., first- and second-order statistics of the three-dimensional velocity vector, at a number of locations and vertical levels within a given area, so that we take into account all relevant motion scales of the atmosphere. For such a purpose, a multiscale modeling approach is needed, in which one starts by downscaling the large scales of atmospheric motions, from, e.g., reanalysis and global forecasts, to the regional or the mesoscales using a numerical weather prediction (NWP) model and continuing down to the microscales through forcing of (nesting to) a Reynolds-averaged Navier–Stokes-like or large-eddy simulation (LES) domain.

Currently, there are a couple of atmospheric modeling systems capable of seamlessly simulating the spatiotemporal behavior of the atmosphere at its multiple scales. One of such is the open-source community-open Weather Research and Forecasting (WRF) model

The value of a WRF-LES-based system can be evaluated by performing real-time multiscale simulations of the atmosphere and subsequent comparison with historical observations (hindcasting). However, such evaluations can be misleading as many aspects of the modeling system play a role in the outputs, such as the uncertainty of the forcing datasets and, for wind in particular, the resolution and accuracy of the topographic inputs, e.g., the resemblance to reality of the land use characteristics and the assignment of roughness length values to predefined land use categories. Due to the difficulty in discerning modeling- from system-related abilities when evaluating real-time simulations, it is important to evaluate results from atmospheric models with observations from sites and conditions resembling canonical flows. If such flows can be observed, the WRF model can be run in an idealized fashion so that the modeler has control on the initial atmospheric boundary layer (ABL) characteristics, topographical inputs, and forcing

From analysis of sonic-anemometer measurements distributed vertically on a 250 m meteorological tower at Østerild, in northern Denmark,

In this study, we first present the methodology (Sect.

We focus our analysis on the accuracy of resolved and modeled atmospheric flow parameters by WRF-LESs through comparison with observations. We include in the comparison vertical profiles of mean wind speed and direction, and velocity variances and covariances, as well as turbulence spectra at various vertical levels.

The measurements at Østerild are described in detail in

We are interested in modeling three types of ABLs: near-neutral (

Figure

We used the LES capability of the WRF model to perform idealized simulations. The WRF model is a non-hydrostatic, fully compressible solver of the Euler equations. It accomplishes LESs by turning off the planetary-boundary-layer scheme options and instead uses one of a number of subgrid-scale (SGS) models. Slip conditions for the horizontal velocity components are imposed at the model top, together with vanishing vertical velocity and fluxes.

Simulations were performed with the WRF model version 4.1.2 to simulate the ABL flow under neutral, unstable, and stable atmospheric conditions; thus we performed one simulation per ABL regime. We used a domain with

Vertical grid spacing as function of vertical level used in the simulations. The vertical level corresponds to the cell height.

The bottom of the domain is flat, and the roughness length was set to the values estimated from the Østerild observations in Sect.

Simulations were initialized assuming a dry atmosphere. For the neutral ABL simulation, the initial temperature was kept constant (289.5 K) up to 700 m, and then an inversion of 10 K km

MOST was applied at the surface through the in-built WRF surface-layer scheme (option 1 in WRF's namelist), although a modification of the open-release scheme was performed to maintain simulations dry. The neutral and unstable ABLs were simulated during 20 and 6 h by imposing a constant surface heat flux

Initial forcing, configuration parameters, and total simulation time for the three types of simulated flows.

The simulations were performed using periodic boundary conditions in both horizontal directions. We output selected variables for a vertical column in the middle of the domain every 1 s and instantaneous values of those variables every 1 h for the positions in the whole domain.

For the three ABL regimes under study, we present an analysis of the simulated transient outputs (Sect.

We need to extract WRF-LES outputs to perform the comparison with the observed statistics at Østerild. The choice of the time to extract LES statistics depends on the type of boundary layer. The analysis is mostly made by performing moving averages over 600 s windows based on the 1 Hz outputs of given variables. We estimate the height of the ABL

Figure

Figure

Figure

Similar to Fig.

In Fig.

Figure

Similar to Fig.

In Fig.

Figure

Instantaneous cross sections (

Figure

Normalized simulated and observed wind profiles for neutral

All simulations match the observed value closest to the surface well, i.e., that at 7 m. When looking within the bulk of the measurement range, we see the strongest deviations from the simulations compared to the mean of the observations under the neutral ABL case. Particularly, within the first

RMSEs of the normalized simulated wind speeds also reflect the qualitative findings (see Table

Figure

Observed and simulated turning of the wind for neutral

For the comparison with the measurements, we need to estimate the total variances and covariances from the WRF-LESs; thus we need to account for the resolved and the subgrid stresses. The total stress is given as

Figure

Simulated and observed vertical profiles of normalized velocity variances

For unstable conditions (see Fig.

Similar to Fig.

For stable conditions (see Fig.

Similar to Fig.

Table

RMSEs of the normalized simulated wind speeds, turning of the wind (rel. dir.), normalized turbulent fluxes, and the total TKE

Figure

Figure

Figure

Neutral velocity spectra at 37

As shown, the observed power spectra are very well behaved at all vertical levels with an inertial subrange slope close to

Under unstable stability conditions (Fig.

Similar to Fig.

Under stable stability conditions (Fig.

Similar to Fig.

To assess the ability of high-fidelity simulations, such as LES, to reproduce the behavior of winds and turbulence within the first hundreds of meters of the ABL, which is useful, e.g., for the siting of wind turbines, we need to try, first, to isolate the effects of physics parametrizations and forcing and, second, to analyze high-quality measurements of both wind and turbulence at several heights. The reason for the former is that such parametrizations and forcing conditions influence the behavior of turbulence, and so it is difficult to differentiate their effects, which are accounted for, e.g., in real-time simulations using mesoscale models, from those inherent to the abilities of LESs. Here, by using wind and turbulence statistics, and velocity spectra computed from sonic-anemometer measurements on a 250 m mast over the predominant wind direction at Østerild, Denmark, we demonstrate that idealized WRF-LESs reproduce the observed wind and turbulence characteristics well, which resemble canonical flow of typical ABL regimes (unstable, neutral, and stable).

Comparison with observations reveals that, under the three ABL regimes, the vertical profiles of normalized wind and direction are well reproduced by the simulations. The simulated means are always within the observed variability, but it should be noted that the latter is large; the observed variability at Østerild is lower than that from the canonical flow observations performed at the 200 m tower at the SWiFT test facility in the US Southern Great Plains

Vertical profiles of observed normalized eddy fluxes are also well reproduced by the simulations. For nearly all vertical levels and for the three ABL regimes, the simulated values are within the observed variability. Under neutral conditions, in particular, the simulated mean normalized velocity variances have an excellent agreement with the observed means specially above 50 m, the best agreement is found under unstable conditions below 100 m, and under stable conditions there is a systematic underestimation of the mean observed values by the simulations above 50 m. For the normalized

Vertical profiles of observed turbulent kinetic energy reveal the highest values under neutral conditions, as expected, due to the high roughness value that was estimated from the observations using MOST and the lowest values under stable conditions. The simulations show the same behavior, although the mean values for both unstable and stable conditions are much closer to each other compared to the observed values. This is because we use the same boundary condition (roughness length) for the unstable and stable simulations, and so the surface-layer scheme in the WRF model computes similar

Simulated and observed velocity spectra match very well within frequencies lower than that corresponding to the effective resolution, which explains the good agreement between simulated and observed velocity variances. Such a good match is found both under the three ABL regimes and the vertical levels examined. As expected due to the nature of the WRF model, the velocity spectra shows a drop-off close to the effective resolution, and so it is only the observed spectra the one that approaches the

Regarding the assumptions made for the simulations we carried out, it is appropriate to reiterate that these are idealized simulations. As such, the initial conditions may not represent observed cases. Observations of the ABL height and observations of vertical profiles of both potential temperature and water vapor mixing ratio within the extent of the ABL are not available at Østerild. The three cases considered here are all characterized by relatively weak surface heat fluxes and strong shear; i.e., they are shear driven. Therefore, assuming a dry atmosphere, i.e., that the moisture effects on the structure of the atmospheric surface layer are small, is a good approximation in the three cases. Since these are idealized simulations, the initial potential profile is well mixed up to 700 m for the neutral and convective boundary layers and up to 100 m for the stably stratified boundary layer. Capping inversions develop naturally due to surface heating or cooling, while the overlaying inversion in the free troposphere is specified. The overlying inversion (10 K km

Note that we cannot guarantee that mesoscale trends embedded in the observations might be increasing the variability on the observed variables and weakening our assumption of homogeneous flow particularly above the surface layer. One way of filtering out periods of strong mesoscale forcing is by deriving mesoscale tendencies from real-time WRF simulations

Given that the comparisons between the outputs of the idealized simulations and the observed statistics are rather good, in future studies we want to explore the ability of a WRF-LES-based multiscale modeling system to simulate in real time the ABL at Østerild and other sites in which high-quality measurements are also available, in more typical unsteady operating conditions. Key issues to address for such purposes include the smoothing effect on turbulence when forcing LES domains with mesoscale information, the modeling of turbulence in intermediate domains when nesting down from mesoscale to LES, and the inherent difficulties of the WRF model in simulating atmospheric flow over terrain steeper than 30–40

Significant progress has been made already in the development of methods to accelerate the development of three-dimensional turbulence in LES domains nested within mesoscale simulations, in neutral

Another important element of multiscale atmospheric simulation involves downscaling through the “gray zone” or “terra incognita” scales

The WRF model's applicability over steep terrain, a known issue when downscaling due to topographic features being better resolved, is likewise being extended, using both higher-order numerical methods

The framework of the present study can be used to assess the utility of the WRF model in these above-described settings to improve wind energy simulations in a broader range of real-world environments and operating conditions, for which smaller-scale flow information, including turbulence, in relation to environmental and meteorological variability, is invaluable to supporting the continued expansion of the wind energy industry.

The numerical outputs were generated with the open-source WRF model (

AP performed the simulations, analyzed both the simulation outputs and observational data, and drafted the manuscript. All authors were involved in the design of the numerical experiments and the proposed methodology. All authors contributed to the revision and finalization of the paper.

The authors declare that they have no conflict of interest.

We acknowledge Javier Sanz Rodrigo and an anonymous reviewer for their suggestions, which improved the paper.

This work is partly funded by the Ministry of Foreign Affairs of Denmark and administered by the Danida Fellowship Centre through the Multi-scale and model-chain Evaluation of Wind Atlases (MEWA) project (grant no. 17-M01-DTU). Jeffrey D. Mirocha's contribution is supported by LLNL under contract DE-AC52-07NA27344 and by the U.S. Department of Energy's Wind Energy Technologies Office.

This paper was edited by Sara C. Pryor and reviewed by Javier Sanz Rodrigo and one anonymous referee.